Training nonlinear parametrizations such as deep neural networks to numerically
approximate solutions of partial differential equations is often based on minimizing a loss …

In recent years, there has been widespread adoption of machine learning-based
approaches to automate the solving of partial differential equations (PDEs). Among these …

Physics-informed machine learning combines the expressiveness of data-based
approaches with the interpretability of physical models. In this context, we consider a …

We develop a provably convergent kernel-based solver for path-dependent PDEs (PPDEs).
Our numerical scheme leverages signature kernels, a recently introduced class of kernels …

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical
systems from time series data. Many methods for such dynamics learning explicitly require …

We study the combination of the alternating direction method of multipliers (ADMM) with
physics-informed neural networks (PINNs) for a general class of nonsmooth partial …

The Koopman operator provides a linear framework to study nonlinear dynamical systems.
Its spectra offer valuable insights into system dynamics, but the operator can exhibit both …

This paper introduces a novel kernel learning framework toward efficiently solving nonlinear
partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that …

This article presents a three-step framework for learning and solving partial differential
equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy …

Gaussian processes (GPs) based methods for solving partial differential equations (PDEs)
demonstrate great promise by bridging the gap between the theoretical rigor of traditional …