Explore cutting-edge research at the intersection of machine learning and dynamical systems through this comprehensive symposium featuring 40 expert presentations. Delve into advanced topics including reservoir computing for climate prediction, Koopman operator theory applications, neural differential equations, and deep learning approaches to nonlinear stability analysis. Examine theoretical foundations such as universal approximation theorems for signature models, representation theory of signature transforms, and optimal transport methods for learning chaotic dynamics. Discover practical applications ranging from weather forecasting and cortical parameter mapping to basin stability estimation and treatment impact prediction. Learn about innovative computational methods including residual dynamic mode decomposition, diffrax numerical solvers, and momentum Stiefel optimizers. Investigate emerging areas like compositional neural network features, rough path theory applications, and multiscale gradient descent techniques. Gain insights into data-driven modeling approaches for complex systems, including reduced order models using invariant manifolds, learning emergent PDEs, and nonparametric kernel methods for interacting particle systems. Access presentations on statistical mechanics approaches to network optimization, spurious minima creation in shallow networks, and stochastic variants of replicator dynamics, providing a comprehensive overview of current research directions in this rapidly evolving interdisciplinary field.

Syllabus

Machine Learning for Prediction of Terrestial Climate and Weather
Transport in Reservoir Computing
Statistics of Attractor Embeddings in Reservoir Computing
Time Shifts to Reduce the Size of Reservoir Computers
Universal Approximation Thms for Continuous Functions of Càdlàg Paths & Lévy-Type Signature Models
A Representation Theoretic View on Signature Transforms
On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos and Other Random...
Koopman Operator Theory Based Machine Learning of Dynamical Systems
Using Statistical Mechanics to Approach the Optimal Size of a Network in Image Recognition
Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computation of Spectral Properties...
Estimation of Interactions among Dynamical Elements by Koopman Operator
Learning Itô Diffusions from Time Series
Emergent Hypernetworks in Oscillator Networks
Learning and Forecasting the Effective Dynamics of Complex Systems across Scales
Learning Emergent PDEs in Learned Emergent Spaces
Learning Reversible Symplectic Dynamics
Combinatorial Topological Dynamics
Data-Driven Reduced Order Models Using Invariant Foliations, Manifolds and Autoencoders
Thoughts on the Future of Governing Equations
A Coarse-Graining Approach to Mapping Cortical Parameter Space
Optimal Transport for Learning Chaotic Dynamics via Invariant Measures
Diffrax: Numerical Differential Equation Solvers in JAX
Dissipative Deep Neural Dynamical Systems
Deep Learning for Nonlinear Stability Analysis in Dynamical Systems
Active Learning in Efficient Estimate for Basin Stability of Dynamic Networks
Predicting the Impact of Treatment over Time with Uncertainty Aware Neural Differential Equations
Approximation Theory of Deep Learning from the Dynamical Viewpoint
r-Adaptivity, Deep Learning and the Deep Ritz Method
A Proximal Method for Sampling
Momentum Stiefel Optimizer, with Applications to Orthogonal Attention, and Optimal Transport
A Stochastic Variant of Replicator Dynamics in Zero-Sum Games and Its Invariant Measures
Creation & Annihilation of Spurious Minima in Shallow Neural Networks
Multiscale Perturbed Gradient Descent: Chaotic Regularization and Heavy-Tailed Limits
Learning Dynamical Systems
Some Time, Some Space, and Some Equations: Machine Learning of Model Error in Dynamical Systems
From Rough Paths to Streamed Data
Compositional Features and Neural Network Complexity for Dynamical Systems
Nonparametric Learning of Interaction Kernels in Interacting Particle Systems
Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces