Upcoming seminars

See the Google Agenda of the seminar, and add the iCal url to your calendar.

• Marios Andreou (University of Wisconsin-Madison),
  Wednesday 10 September at 14:30, Room TBD

  Title: Harnessing the Conditional Gaussian Nonlinear System Framework for Efficient Adaptive-Lag Online Smoothing and Causal Inference

  This talk presents recent advances in data assimilation and causal inference through the Conditional Gaussian Nonlinear System (CGNS) framework. This is a class of nonlinear stochastic models in which, conditioned on a subset of state variables, the unobserved components follow a Gaussian posterior distribution. This structure enables efficient Bayesian state estimation and sampling via closed-form solutions, making CGNS especially suitable for high-dimensional, multiscale systems with regime shifts and intermittent extreme events. CGNSs have wide applications in uncertainty quantification, modelling complex geophysical phenomena, dealing with high-dimensional systems, and facilitating machine learning.

  We first introduce an adaptive-lag online smoother that leverages the analytical tractability of CGNSs to effectively reduce the computational storage requirements of standard smoothing procedures. Adaptively adjusting the lag by exploiting information-theoretic criteria, this strategy is applicable to turbulent systems with time-varying temporal correlations and performs well in challenging real-world problems such as Lagrangian data assimilation and online parameter estimation.
  Building on this, we present a paradigm-shifting causal inference framework, called Assimilative Causal Inference (ACI), which leverages Bayesian data assimilation to trace causes backward from observed effects by solving an inverse problem rather than quantifying forward influence. It uniquely identifies dynamic causal interactions without requiring observations of candidate causes, accommodates short datasets, and scales efficiently to high dimensions. Crucially, it provides online tracking of causal roles, which may reverse intermittently, and facilitates a mathematically rigorous criterion for the causal influence range, revealing how far effects propagate. ACI opens new avenues for studying complex systems, where transient causal structures are critical. Despite its general setting, within the CGNS framework ACI enables explicit nil-causality principles and analytical characterisations of the associated causal influence ranges for objective temporal attribution and prediction.
  Applications to systems showcasing turbulent dynamics and nonlinear geophysical flows illustrate how CGNSs provide scalable, real-time, and theoretically grounded solutions to online smoothing and causal inference.

• Laure Saint-Raymond (IHES),
  Wednesday 10 September at 14:30, Room TBD

  Title TBD

  Abstract TBD

• Charles Bertucci (École polytechnique),
  Thursday 2 October at 10:30, Room TBD

  Title TBD

  Abstract TBD

Past seminars (2024-2025)

• Borjan Geshkovski (Inria MEGAVOLT), October 16th, 15:00pm, Room B211.

  Dynamic metastability in the self-attention model

  The pure self-attention model is a simplification of the celebrated Transformer architecture, which neglects multi-layer perceptron layers and includes only a single inverse temperature parameter. The model exhibits a remarkably similar qualitative behavior across layers to that observed empirically in a pre-trained Transformer. Viewing layers as a time variable, the self-attention model can be interpreted as an interacting particle system on the unit sphere. We show that when the temperature is sufficiently high, all particles collapse into a single cluster exponentially fast. On the other hand, when the temperature falls below a certain threshold, we show that although the particles eventually collapse into a single cluster, the required time is at least exponentially long. This is a manifestation of dynamic metastability: particles remain trapped in a “slow manifold” consisting of several clusters for exponentially long periods of time. Our proofs make use of the fact that the self-attention model can be written as the gradient flow of a specific interaction energy functional previously found in combinatorics.

• Olivier Zahm (Inria AIRSEA), October 28th, 10:00am, Room B211.

  Preconditioning Langevin dynamics via optimal Riemannian Poincaré inequalities

  The Poincaré inequality is a key property for the convergence analysis of many practical algorithms, including MCMC samplers, dimension reduction methods etc. In this talk, we introduce a Riemannian version of the Poincaré inequality where a positive definite weighting matrix field (i.e. a Riemannian metric) is introduced to improve the Poincaré constant, and therefore the convergence speed of the resulting preconditioned Langevin dynamics. By leveraging the notion of *moment measure*, we prove the existence of an optimal metric which yields a Poincaré constant of 1. This optimal metric turns out to be a *Stein kernel*, offering a novel perspective on these complex but central mathematical objects that are hard to obtain in practice. We also present an implementable optimization algorithm to numerically obtain the optimal metric. The method’s effectiveness is illustrated through simple but non-trivial examples which reveals rather complex solutions. Lastly, we show how to design efficient Langevin-based sampling schemes which enables rapid jump across various modes and tails of the measure to be sampled from.

• Theron Guo (MIT, visiting MATHERIALS in October and November), November 7th, 10:00am, Room B211.

  Model order reduction for computational homogenization in nonlinear solid mechanics

  Computational homogenization has become an indispensable method to establish the effective properties of microstructures and efficiently solve multiscale problems in solid mechanics. However, the resulting two-scale problem remains computationally expensive for nonlinear problems and is typically infeasible in multi-query contexts, such as optimization or uncertainty quantification. To alleviate the high computational costs, model order reduction techniques can be used. In this talk, I will introduce different variants of computational homogenization, and illustrate the effectiveness of projection-based model order reduction for two variants.

• Maria Laura Delle Monache (UC Berkeley), Thursday November 28th, 10:00am, Room B211.

  Control Strategies for Mixed Autonomy Traffic: theory, simulations and real-life experiments.

  The recent and rapid emergence of disruptive technologies is dramatically changing how traffic is monitored and managed in our cities. They will contribute to generate new knowledge and capabilities to design and implement innovative transport policies. In this talk, we will show how we can exploit new technologies to improve traffic management. We will focus on control strategies for traffic systems with the aid of small fleets of connected and automated vehicles immersed in human driven traffic flow. We present a class of coupled PDE-ODE models describing the interaction of autonomous vehicles (AVs) with the surrounding traffic. The model consists of a scalar conservation law for the main traffic flow, coupled with ordinary differential equations describing the possibly interacting AV trajectories. We will prove analytically and numerically how the proposed control theory can improve traffic performance and finally, we will present the MegaVanderTest, a test involving 100 connected and automated vehicles (CAVs). The MegaVanderTest is to our knowledge the field test which achieved the largest concentration of CAVs collaboratively controlling traffic on a single stretch of freeway.

• Andy Philpott (University of Auckland), Monday December 2nd, 14:00, Room B211.

  10 Challenges for mathematical modeling of energy transition

  The Architecture of Green Energy Systems program was a 10-week joint research project funded by the Institute of Mathematical and Statistical Innovation at the University of Chicago in the summer of 2024. An outcome of this project was a draft review paper based on discussions of participants at the closing workshop. This paper identifies ten challenges for the mathematical modelling community that will be crucial to address in planning and implementing the transition to a net-zero carbon energy system.

  In this talk I will give a broad overview of the challenges that were identified with a focus on modelling challenges arising in the conversion of household, transport and industrial energy use to renewable electricity. This will require enormous investments in renewable electricity generation, storage and transmission. I will give some examples of models used to help plan this process, and discuss the challenges that still have to be addressed to make the models useful to policy makers, regulators and investors.

• Immanuel Bomze (Univ. Vienna), Monday December 2nd, 15:30, Room B211.

  First-order methods for the impatient – support identification in finite time with Frank/Wolfe-variants

  We study active set identification results for the away-step Frank-Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result.  We then prove, in the nonconvex case, a novel $O(1/\sqrt{k})$ convergence rate result and active set identification for different step sizes (under suitable assumptions on the set of stationary points). By exploiting those results, we also give explicit active set complexity bounds for both strongly convex and nonconvex objectives. While we initially consider the probability simplex as feasible set, time permitting we show how to adapt some of our results to generic polytopes. A particular case with interesting applications covers projection-free methods on product domains.

• Feliks Nüske (Max Planck Institute), Tuesday December 17th, 10:00am, Room B211.

  Approximating Metastable Dynamics with Random Fourier Features

  Metastablility is a phenomenon which often inhibits the efficient simulation of dynamical systems, or the generation of samples from high-dimensional probability measures. In particular, metastability is frequently encountered in computer simulations of biological macromolecules using molecular dynamics. It is well-known that metastable transitions and their time scales are encoded in the dominant spectrum of certain transition operators, also called Koopman operators. The study of Koopman operators, and their data-driven approximation by algorithms like the Extended Dynamic Mode Decomposition (EDMD), have gained significant traction in the study of dynamical systems, and have led to widespread application.
  In this talk, I will report on recent progress concerning the data-driven analysis of metastable systems using Koopman operators. First, I will introduce approximation methods on reproducing kernel Hilbert spaces (RKHS), which allow the use of rich approximation spaces, and explain how the resulting large-scale linear problems can be solved efficiently using random Fourier features (RFF). Second, I will explain how similar ideas can be applied to learn models for the infinitesimal generator, which allows for a more detailed system analysis, including the definition of coarse grained models.

• Richard Kraaij (TU Delft), Thursday December 19th, 10:00am, Room B211.

  Well-posedness for Hamilton-Jacobi equations for stochastic control problems: A new view on the classical approach using couplings

  Stochastic control problems for controlled Markov processes can be infinitesimally characterized using a second order Hamilton-Jacobi-Bellman (HJB) equation. The classical work of Crandall-Ishii-Lions (1992) establishes how to obtain uniqueness of viscosity solutions for controlled diffusion processes, and a collection of recent works has pushed the estimates to include classes of spatially inhomogeneous controlled Lévy processes.

  We introduce a new perspective of the classical proof methods in terms of Markovian couplings, putting both sets of results mentioned above in a common framework. The new perspective also enables an approach in new contexts, e.g. in that of Riemannian manifolds, which, if time allows, I will briefly discuss.

  Based on joint work with Serena Della Corte (Delft), Fabian Fuchs (Bielefeld) and Max Nendel (Bielefeld) and work in progress with Karen Habermann (Warwick) Rik Versendaal (Delft).

• Raphaël Barboni (ENS Ulm), Thursday January 9th, 10:00am, Room TBD.

  Understanding the training of infinitely deep and wide ResNets with Conditional Optimal Transport

  We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to the non-convexity and the non-coercivity of the objective. Yet, in applications, those tasks are successfully solved by simple optimization algorithms such as gradient descent. To better understand this phenomenon, we focus here on a “mean-field” model of infinitely deep and arbitrarily wide ResNet, parameterized by probability measures over the product set of layers and parameters and with constant marginal on the set of layers. Indeed, in the case of shallow neural networks, mean field models have proven to benefit from simplified loss-landscapes and good theoretical guarantees when trained with gradient flow for the Wasserstein metric on the set of probability measures. Motivated by this approach, we propose to train our model with gradient flow w.r.t. the conditional Optimal Transport distance: a restriction of the classical Wasserstein distance which enforces our marginal condition. We first show the well-posedness of the gradient flow equation and then its local convergence around well-chosen initializations. This is joint work with G.Peyré and F.-X. Vialard.

• Pierre-Cyril Aubin (CERMICS), Thursday January 16th, 10:30am, Room B211.

  EVIs and gradient descent with c(x,y) cost, and alternating minimization

  How to go beyond the square distance d^2 in optimization algorithms and flows in metric spaces? Replacing it with a general cost function c(x,y) and using a majorize-minimize framework I will detail a generic class of algorithms encompassing Newton/mirror/natural/Riemannian gradient descent by reframing them as an alternating minimization, each for a different cost c(x,y). Rooted in cross-differences, the convergence theory to the infimum and to the continuous flow is investigated is based on a (discrete) evolution variational inequality (EVI) which enjoys similar properties to the EVI with d^2 regularizer. This provides a theoretical framework for studying splitting schemes beyond the usual implicit Euler in gradient flows. This talk is based on works with Flavien Léger (INRIA Paris), Giacomo Sodini and Ulisse Stefanelli (Uni Vienna).

• Guillaume Chennetier (CERMICS), Thursday January 30th, 10:30am, Room B211.

  Graph-informed importance sampling for piecewise deterministic Markov processes. Application in reliability assessment.

  Piecewise Deterministic Markov Processes (PDMPs) describe deterministic dynamical systems with parameters subject to random jumps, making them versatile tools for modeling complex phenomena. However, generating their trajectories can be computationally expensive. For a large class of inference problems, an optimal sampling strategy exists and relies on a generalized version of the “committor function” of the process. We propose a novel adaptive importance sampling method to efficiently generate rare trajectories of PDMPs. The approach involves a two-phase process. In a first offline phase, the PDMP is approximated by a simpler process on a graph, enabling explicit computation of key quantities used to build a low-cost approximation of the committor function. In a second online phase, PDMP trajectories are generated using a distribution informed by this approximation and iteratively refined via cross-entropy minimization. We provide asymptotic guarantees and demonstrate the method’s effectiveness by estimating the failure probability of a complex industrial system.

• Panos Parpas (Imperial College), Wednesday February 5th, 10:30am, B211.

  Stochastic Mirror Descent for Convex Optimization with Consensus Constraints

  The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed optimization problems has not been previously addressed. In this talk we present an exact distributed mirror descent algorithm in continuous-time under additive noise. We establish a linear convergence rate of the proposed dynamics for the setting of convex optimization. Our analysis draws motivation from the Augmented Lagrangian and its relation to gradient tracking. To further explore the benefits of mirror maps in a distributed setting we present a preconditioned variant of our algorithm with an additional mirror map over the Lagrangian dual variables. This allows our method to adapt to both the geometry of the primal variables, as well as to the geometry of the consensus constraint. We also propose a Gauss-Seidel type discretization scheme for the proposed method and establish its linear convergence rate. For certain classes of problems we identify mirror maps that mitigate the effect of the graph’s spectral properties on the convergence rate of the algorithm. Using numerical experiments we demonstrate the efficiency of the methodology on convex models, both with and without constraints. Our findings show that the proposed method outperforms other methods, especially in scenarios where the model’s geometry is not captured by the standard Euclidean norm.

  Joint work with: A. Borovykh, N. Kantas, and G.A Pavliotis

• Emma Horton (University of Warwick), Wednesday February 19th at 10:00, Room B211

  Monte Carlo methods for branching processes

  Branching processes naturally arise as pertinent models in a variety of situations such as cell division, population dynamics and nuclear fission. For a wide class of branching processes, it is common that their first moment exhibits a Perron Frobenius-type decomposition. That is, the first order asymptotic behaviour is described by a triple $(\lambda, \varphi, \eta)$, where $\lambda$ is the leading eigenvalue of the system and $\varphi$ and $\eta$ are the corresponding right eigenfunction and left eigenmeasure respectively. Thus, obtaining good estimates of these quantities is imperative for understanding the long-time behaviour of these processes. In this talk, we discuss various Monte Carlo methods for estimating this triple. This talk is based on joint work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).

• Eloi Tanguy (Université Paris-Cité), Thursday March 6th, 9:30am, Room B211.

  Computing Barycentres of Measures for Generic Transport Costs [Slides]

  Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use Sinkhorn iterations, where an entropic regularisation term is introduced to make the problem more manageable. Another approach involves using fixed-point methods, akin to those employed for computing Fréchet means on manifolds. The convergence of such methods for 2-Wasserstein barycentres, specifically with a quadratic cost function and absolutely continuous measures, was studied by Alvarez-Esteban et al. (2016). We delve into the main ideas behind this fixed-point method and explore how it can be generalised to accommodate more diverse transport costs and generic probability measures, thereby extending its applicability to a broader range of problems, including Gaussian Mixture Models. We show convergence results for this approach and illustrate its numerical behaviour on several barycentre problems.

• Romain Cosson (Inria Paris), Thursday March 13th, 14:00pm, Room B211.

  Can we parallelize maze solving? Can we find a short path, without a map?

  In this talk, we will explore two intriguing problems within the framework of competitive analysis: a methodology developed since the 1990s to study algorithms in the face of uncertainty. I will first introduce key concepts such as « regret » and « competitive ratio » through classical examples. Then, I will present new results for the two questions posed in the title, which are known in the literature as « layered graph traversal » and « collective tree exploration ». We will use these problems as a case study of the technical challenges that appear in online algorithms. Additionally, I will highlight emerging directions in the field, including collective algorithms, entropic regularization and average-case analysis.

• Jan Zeman (Czech Technical University in Prague), March 26, 10:00am, Room B211.

  PDE preconditioning perspective on FFT-accelerated solvers for micromechanics [Slides]

  The use of spectral trigonometric solvers in image-based computational micromechanics, first introduced by Moulinec and Suquet [1], has gained popularity due to their computational efficiency, low memory requirements, and ease of implementation. In this talk, I will focus on the Finite Element (FE)-based reformulation of the original scheme as developed by Schneider et al. [2] and Leuschner and Fritzen [3]. Specifically, I will (1) provide a linear algebra perspective on their advances and (2) relate them to recent developments in Laplace preconditioning of elliptic partial differential equations [4].

  The approach we adopted in [5] involves preconditioning the periodic corrector problem using a discrete Green’s operator derived from a reference problem with constant coefficients. Theoretical analysis indicates that the eigenvalues of the preconditioned matrix can be bounded both above and below by the coefficients of the original and reference problems. This property allows the system to be solved by the preconditioned conjugate gradient method with a number of iterations that are nearly independent of the grid size.

  From a computational standpoint, we exploit the fact that for regular meshes, the system matrix of the reference problem has a block-diagonal structure in Fourier space. This structure allows for efficient inversion using Fast Fourier Transform (FFT) techniques. As a result, the computational complexity of our scheme is primarily determined by the FFT, making it comparable to that of spectral solvers. Unlike trigonometric spectral solvers, our proposed scheme is compatible with arbitrary finite element shape functions with local support and does not suffer from the Fourier ringing phenomenon.

  This is a joint work with Ivana Pultarová (Czech Technical University in Prague) and Martin Ladecký (University of Freiburg).

  References:
  [1] Moulinec, H. and Suquet. P. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. C. R. Acad. Sci. Paris (1994) 318(11):1417–1423, hal-03019226.
  [2] Schneider, M. and Merkert, D. and Kabel, M. FFT-based homogenization for microstructures discretized by linear hexahedral elements. Int. J Numer. Methods Eng. (2017) 109:1461–1489.
  [3] Leuschner, M. and Fritzen, F. Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems. Comput. Mech. (2018) 62(3):359–392.
  [4] Nielsen, B.F. and Strakoš, Z. A simple formula for the generalized spectrum of second order self-adjoint differential operators. SIAM Rev. (2024) 66(1):125–146.
  [5] Ladecký M. et al. An optimal preconditioned FFT-accelerated finite element solver for homogenization. Appl. Math. Comput. (2023) 446:127835, arXiv:2203.02962.
  

• Wei Zhang (Zuse Institute Berlin), Monday 7 April, 10:30am, Room B211.

  Some mathematical understanding of deep-learning techniques for identifying collective variables of molecular dynamics

  High-dimensional metastable molecular dynamics can often be characterized by a few features of the system, i.e. collective variables (CVs). Various data-driven methods have been developed in recent years for identifying collective variables of molecular dynamics. In this talk, I will discuss two representative deep learning-based methods from a mathematical perspective.The first method employs autoencoders to minimize reconstruction error and is a dimensionality reduction method for static data, whereas the second method computes eigenfunctions of certain operator associated to the underlying dynamics that encode dynamical properties of the underlying system. I will present concrete learning algorithms and illustrate them on numerical examples.

• Yuxi Hu, Tuesday 15 April at 10:30, Room V306.

  Initial boundary value problem for relaxed compressible Navier-Stokes-Fourier equations

  We investigates an initial boundary value problem for the relaxed one-dimensional compressible Navier-Stokes-Fourier equations. By transforming the system into Lagrangian coordinates, the resulting formulation exhibits a uniform characteristic boundary structure. We first construct an approximate system with non-characteristic boundaries and establish its local well-posedness by verifying the maximal nonnegative boundary conditions. Subsequently, through the construction of a suitable weighted energy functional and careful treatment of boundary terms, we derive uniform a priori estimates, thereby proving the global well-posedness of smooth solutions for the approximate system. Utilizing these uniform estimates and standard compactness arguments, we further obtain the existence and uniqueness of global solutions for the original system. In addition, the global relaxation limit is established. The analysis is fundamentally based on energy estimates

• Yohann de Castro (Camille Jordan, Lyon), Wednesday 30 april 10:30am, Room B211.

  FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures.

  In this talk, we present a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to scale Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse optimisation problems on measures. By formulating CPGD steps within a variational framework, we establish a global convergence showcasing the efficiency and effectiveness of our algorithm. Several comments and applications will help us to understand the applications of this algorithm in Machine Learning and Signal Processing. Based on joint work with S. Gadat (TSE) and C. Marteau (Lyon1), «  FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures. » A key reference is a nice paper of Lénaïc Chizat,  «  Sparse Optimization on Measures with Over-parameterized Gradient Descent ».  A closely related line of work has been presented at the last ICM by Francis and Lenaïc.

• Mouad Ramil (Inria SIMSMART, Rennes), Jeudi 15 mai à 13h00, Room TBD.

  Eyring-Kramers law for the underdamped Langevin process

  The Eyring-Kramers (EK) law describes the asymptotic of the mean transition time between basins of a potential function when the temperature is low. The EK law was obtained first for the overdamped Langevin process and was recently extended to non-reversible elliptic diffusion processes. However, the scheme of proof relies on Potential theory tools which are ill-defined when considering non-elliptic diffusion process. In this presentation, we will talk about a recent work in collaboration with S. Lee and I. Seo (Seoul National University) where we extend the EK law for the underdamped Langevin process, which is a non-elliptic and non-reversible diffusion process, by implementing a novel approach which circumvents the previous technicalities.

• Jean-Luc Guermond (Texas A&M University), Thursday May 22nd, 10:00am, Room F103.

  Approximation des involutions pour les systèmes de lois de conservation

  Je vais présenter quelques résultats récents sur l’approximation des lois de conservation en insistant plus particulièrement sur les involutions. Les involutions sont des propriétés induites par la structure des opérateurs différentiels intervenant dans les lois de conservation, telles que la loi de Gauss pour les équations de Maxwell ou la magnétohydrodynamique. Préserver la structure des involutions est essentiel pour garantir la stabilité en temps long des approximations numériques. Je donnerai des résultats récents pour l’approximation par éléments finis discontinus et éléments finis continus.

• Sibo Cheng (CEREA), Wednesday May 28th, 10:30am, Room B211.

  Hybrid data assimilation and machine learning algorithms for sparse observational data

  Reconstructing spatiotemporal systems from sparse observations remains a long-standing challenge in several domains, including geoscience, air pollution and fluid dynamics. While various data assimilation (DA) and machine learning (ML) methods have shown potential, they still face significant challenges (see [1]): (i)The computational burden of conventional DA algorithms (including error covariance specification), particularly for multivariate, high-dimensional systems. (ii) Sparse and movable sensor placement, which makes conventional ML models (typically requiring fixed and regularly distributed input data) cumbersome. (iii) The ill-defined nature of the sparse reconstruction problem, which poses significant risks of overfitting.
  We will present our recent works aimed at addressing these challenges. More specifically, we developed latent DA algorithms to reduce the computational burden of variational DA methods. These algorithms demonstrate great potential in efficiently assimilating sparse observations within a reduced-order latent space constructed by neural networks, thanks to the TorchDA library [2]. The latter enables GPU implementation of mainstream data assimilation methods and supports non-explicit state-observation transformation functions, provided they can be learned by a neural network.
  We have also employed advanced deep learning techniques, including Voronoi-tessellation CNNs [3], Vision Transformer-based autoencoders and diffusion-based generative models [4], to learn mappings from sparse observations to the complete physical space. These approaches effectively address challenges such as movable sensor placements and varying sensor numbers. Their integration with DA algorithms has also been evaluated. The numerical results tested on cases ranging from fluid dynamics benchmarks to air pollution and hydrology simulations will also be discussed.

• Theron Guo (MIT, visiting MATHERIALS in October and November), Monday June 2nd at 11:00am, en salle 15-16 309 at Jussieu.

  Mathematical Modeling and Error Estimation for the Thermal Dunking Problem

  We consider the so-called Dunking problem often encountered in engineering heat transfer: a passive solid body at uniform initial temperature T_i is suddenly immersed in a fluid environment at temperature T_\infty. The key quantity of interest is the temperature evolution of the solid over time, driven by heat exchange with the surrounding fluid. The high-fidelity mathematical model of this process is a conjugate heat transfer model — a coupled fluid-solid system that resolves both the internal conduction within the solid and the convective transport in the fluid. Due to its complexity, it is seldom used in practice. Instead, practitioners often employ the lumped capacitance model, a simplified ODE that approximates the average temperature of the solid. This model assumes spatially uniform temperature within the solid and relies on a prescribed heat transfer coefficient, a parameter typically obtained from empirical correlations or experimental data for standard geometries and flow conditions. In this talk, we first study the model error associated with the lumped capacitance approximation in regard to the geometry of the solid and nonuniformity of the external flow. We then discuss ongoing work aimed at directly predicting the heat transfer coefficient from flow and geometric features. This is joint work with Kento Kaneko (MIT), Claude Le Bris (ENPC & Inria), and Anthony T Patera (MIT).

• Sharon Di (Columbia University), Thursday June 5th, 10:30am, Room B211.

  AI-Powered Safety-Aware Urban Transportation Digital Twin

  Transportation digital twins have become increasingly popular tools to improve traffic efficiency and safety. However, the majority of effort nowadays is focused on the “eyes” of the digital twin, which is object detection using computer vision. I believe the key to empowering the intelligence of a transportation digital twin lies in its “brain,” namely, how to utilize the information extracted from various sensors to infer traffic dynamics evolution and devise optimal  control and management strategies with real-time feedback to guide the transportation ecosystem toward a social optimum. My current research interest lies in employing foundational models (such as Vision-Language Models (VLMs) and Large Language Models (LLM)) and GenAI (such as diffusion models), to create an urban transportation digital twin that simulates urban traffic scenarios and optimizes traffic management strategies. The applications range from pedestrian safety warning, adaptive traffic signal control, autonomous driving, to micromobility detection and tracking.

  In this talk, I plan to introduce tools including machine learning and game theory to develop an urban transportation digital twin, leveraging data collected from the NSF PAWR COSMOS city-scale wireless testbed being deployed in West Harlem next to the Columbia campus. In this talk, I will primarily focus on two solutions: (1) scientific machine learning that leverages both domain knowledge and available data, and (2) mean field game that bridges the gap between micro- and macroscopic behaviors of multi-agent dynamical systems. In the first topic, physics-informed deep learning will be introduced and applied to traffic state estimation and uncertainty quantification. In the second topic, I will introduce how to model behaviors of new actors (e.g., a large number of autonomous vehicles) in a transportation system and their interaction with existing actors (e.g., human-driven vehicles).

• Tito Homem-de-Mello (Universidad Adolfo Ibañez, Santiago, CHILE), Thursday June 12th, 10:30am, Room B211.

  Data Driven Optimization: Models and Applications

  In recent years we have seen an explosion of the use of data to make decisions, and as a result many data-driven approaches for optimization have been developed. In this talk we will discuss some new models and applications of these techniques. We will focus in particular on a class of approaches that have gained attention in the literature recently, which integrate machine learning methods for estimation from data and the optimization model. Such integration can be accomplished in several ways, but the methods typically fall into one of two categories: sequential (i.e., open-loop) methods, and closed-loop ones. Naturally, new challenges arise from these approaches. We discuss some of these challenges,  techniques that can be used, and present a few practical examples where these ideas can be used.

• Eric Chung (University of Hong Kong), Thursday June 19th, 14:00 pm, Room F107.

  Multiscale finite element methods, their generalization and applications

  In this talk, I will give an overview of the multiscale finite element methods. The general idea is to use some pre-computed multiscale basis functions coupled with some variational formulations to solve multiscale PDEs. For challenging problems, we introduced some generalizations. The idea is to use local spectral problems to identify dominant modes, which will be used as multiscale basis functions. We will also discuss a few applications.

• Jean-Guillaume de Damas (Inria Paris, équipe Alpines), Wednesday June 25th, 10:30pm, Room B211.

  Randomized methods for the eigenvalue problem and low rank approximation

  Randomization in numerical linear algebra is a dimension-reduction technique used to speed up calculations in many algorithms. In particular, it is used to obtain orthogonal bases of large subspaces such as Krylov subspaces. In this talk, I will discuss how random orthogonalization processes can be used to solve the eigenvalue problem for a few eigenpairs or to obtain a low-rank approximation of a matrix. To this end, I will introduce two methods: the randomized implicitly restarted Arnoldi (rIRA) and its extension, the randomized Krylov Schur (rKS). We will discuss their numerical efficiency and the advantages of using randomization.