Explore advanced mathematical concepts and their applications through this comprehensive workshop featuring expert presentations on neural networks, optimization algorithms, and computational mathematics. Delve into cutting-edge research topics including neural networks from numerical analysis perspectives, units-equivariant machine learning, and perturbations of orthogonal polynomials using Riemann-Hilbert problems. Learn about blackbox optimization techniques with MADS algorithms and NOMAD software, efficient implicit differentiation methods, and the expressivity of deep neural networks. Discover variational analysis fundamentals, deep learning approaches for solving differential equations on orientable surfaces, and physics-informed neural networks. Examine topics in nonconvex optimization, experimental continuation methods for nonlinear structures, and stochastic optimization under deterministic constraints. Investigate signal recovery with generative priors, depth-adaptive neural networks from optimal control viewpoints, and Rayleigh quotient optimizations for eigenvalue problems. Study parallel-in-time numerical solutions for PDEs, primal-dual algorithms for risk minimization, and sparse spectral methods for power-law interactions. Gain insights into optimization on spheres, algorithmic stability for machine learning generalization, agent-based models and their continuum limits, and data-driven supervised learning with uncertainty quantification. Access specialized videoconference sessions on bifurcation detection from noisy time series and ultraspherical spectral methods.

Syllabus

Bruno Després: Neural Networks from the viewpoint of Numerical Analysis
Soledad Villar: Units-equivariant machine learning
Tom Trogdon: Perturbations of orthogonal polynomials: Riemann-Hilbert problems, random matrices ...
Sebastien Le Digabel: Blackbox optimization with the MADS algorithm and the NOMAD software
Fabian Pedregosa: Efficient and Modular Implicit Differentiation
David Rolnick: Expressivity and learnability in deep neural networks
Matus Benko: Variational Analysis: Basics, Calculus, and Semismoothness*
Alex Bihlo: Deep neural networks for solving differential equations on general orientable surface
Degenerate singular cycles and chaotic switching in the two-site open Bose--Hubbard model
Equidistant and non equidistant pulsing patterns in an excitable microlaser with delayed feedback
Deep learning of conjugate mappings
Hidden convexity in nonconvex optimization
Les mathématiques ont une histoire et une géographie
Experimental continuation of nonlinear load-bearing structures
Algorithms for Deterministically Constrained Stochastic Optimization
Some Thoughts on Physics Informed Neural Networks
On LASSO parameter sensitivity
The Modern Mathematics of Deep Learning
Nonlinear reduced models for parametric PDEs
Mathematical Foundations of Robust and Distributionally Robust Optimization
From differential equations to deep learning for image analysis
Depth-Adaptive Neural Networks from the Optimal Control viewpoint
Signal Recovery with Generative Priors
Targeted use of deep learning for physics and engineering
Rayleigh quotient optimizations and eigenvalue problems
Optimal approximation for unconstrained non-submodular minimization
Halting Time is Predictable for Large Models: A Universality Property and Average-case Analysis
Parallel-in-time numerical solution of time-dependent PDEs
A Primal-Dual Algorithm for Risk Minimization in PDE-Constrained Optimization
Optimality in Optimization
Variational Perspectives on Mathematical Optimization
Sparse Spectral Methods for Power-Law Interactions
Optimization on Spheres : Models and Proximal Algorithms with Computational Performance Comparisons
Algorithmic stability for generalization guarantees in machine learning
Simple agent-based models and their continuum limit
Data-driven supervised learning: Neural networks and uncertainty quantification
Videoconference: Detecting and distinguishing bifurcations from noisy time series data
Videoconference: The Ultraspherical Spectral Method