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Tue Dec 14 05:00 AM -- 01:45 PM (PST)
The Symbiosis of Deep Learning and Differential Equations
Luca Celotti · Kelly Buchanan · Jorge Ortiz · Patrick Kidger · Stefano Massaroli · Michael Poli · Lily Hu · Ermal Rrapaj · Martin Magill · Thorsteinn Jonsson · Animesh Garg

Workshop Home Page

Deep learning can solve differential equations, and differential equations can model deep learning. What have we learned and where to next?

The focus of this workshop is on the interplay between deep learning (DL) and differential equations (DEs). In recent years, there has been a rapid increase of machine learning applications in computational sciences, with some of the most impressive results at the interface of DL and DEs. These successes have widespread implications, as DEs are among the most well-understood tools for the mathematical analysis of scientific knowledge, and they are fundamental building blocks for mathematical models in engineering, finance, and the natural sciences. This relationship is mutually beneficial. DL techniques have been used in a variety of ways to dramatically enhance the effectiveness of DE solvers and computer simulations. Conversely, DEs have also been used as mathematical models of the neural architectures and training algorithms arising in DL.

This workshop will aim to bring together researchers from each discipline to encourage intellectual exchanges and cultivate relationships between the two communities. The scope of the workshop will include important topics at the intersection of DL and DEs.

Introduction and opening remarks (Introduction)
Neha Yadav - Deep learning methods for solving differential equations (Invited Talk)
Contributed Talk 1 (Contributed Talk)
Coffee Break (Break)
Poster Spotlights 1 (Poster Spotlights)
Poster Session 1 (Poster Session)
Philipp Grohs - The Theory-to-Practice Gap in Deep Learning (Invited Talk)
Coffee Break (Break)
Panel Discussion
Lunch Break (Break)
Weinan E - Maximum principle-based algorithm for deep learning (Invited Talk)
Contributed Talk 2 (Contributed Talk)
Coffee Break (Break)
Poster Spotlights 2 (Poster Spotlights)
Poster Session 2 (Poster Session)
Anima Anandkumar - Neural operator: A new paradigm for learning PDEs (Invited Talk)
Contributed Talk 3 (Contributed Talk)
Contributed Talk 4 (Contributed Talk)
Final Remarks
Empirics on the expressiveness of Randomized Signature (Poster)
Neural Solvers for Fast and Accurate Numerical Optimal Control (Spotlight)
A neural multilevel method for high-dimensional parametric PDEs (Poster)
Shape-Tailored Deep Neural Networks With PDEs (Poster)
Data-driven Taylor-Galerkin finite-element scheme for convection problems (Poster)
Expressive Power of Randomized Signature (Poster)
Multigrid-augmented deep learning preconditioners for the Helmholtz equation (Poster)
Gotta Go Fast with Score-Based Generative Models (Poster)
Beltrami Flow and Neural Diffusion on Graphs (Spotlight)
Scaling physics-informed neural networks to large domains by using domain decomposition (Poster)
Spectral PINNs: Fast Uncertainty Propagation with Physics-Informed Neural Networks (Poster)
Parametric Complexity Bounds for Approximating PDEs with Neural Networks (Spotlight)
Non Vanishing Gradients for Arbitrarily Deep Neural Networks: a Hamiltonian System Approach (Poster)
Learning Implicit PDE Integration with Linear Implicit Layers (Spotlight)
On Second Order Behaviour in Augmented Neural ODEs: A Short Summary (Poster)
Uncertainty Quantification in Neural Differential Equations (Poster)
Actor-Critic Algorithm for High-dimensional PDEs (Poster)
NeurInt-Learning Interpolation by Neural ODEs (Spotlight)
Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal (Spotlight)
Layer-Parallel Training of Residual Networks with Auxiliary Variables (Poster)
Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization (Poster)
Fitting Regularized Population Dynamics with Neural Differential Equations (Poster)
Neural ODE Processes: A Short Summary (Spotlight)
Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs (Poster)
Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks (Poster)
Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations (Spotlight)
Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint (Poster)
Sparse Gaussian Processes for Stochastic Differential Equations (Poster)
HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks (Poster)
Adversarial Sampling for Solving Differential Equations with Neural Networks (Poster)
Accelerated PDEs for Construction and Theoretical Analysis of an SGD Extension (Poster)
GRAND: Graph Neural Diffusion (Poster)
Quantized convolutional neural networks through the lens of partial differential equations (Poster)
MGIC: Multigrid-in-Channels Neural Network Architectures (Poster)
Investigating the Role of Overparameterization While Solving the Pendulum with DeepONets (Poster)