Related papers: Latent Generative Solvers for Generalizable Long-T…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…

Generative Flow Networks (GFNs) were initially introduced on directed acyclic graphs to sample from an unnormalized distribution density. Recent works have extended the theoretical framework for generative methods allowing more flexibility…

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES…

This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revisiting the classical Lyapunov method and the standard…

Physics simulators are essential in science and engineering, enabling the analysis, control, and design of complex systems. In experimental sciences, they are increasingly used to automate experimental design, often via combinatorial search…

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data generating process is based on physical processes these…

Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

Physics-integrated generative modeling is a class of hybrid or grey-box modeling in which we augment the the data-driven model with the physics knowledge governing the data distribution. The use of physics knowledge allows the generative…

Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between…

Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD),…

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song…

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and…

Accurately predicting counterfactual user feedback is essential for building effective recommender systems. However, latent confounding bias can obscure the true causal relationship between user feedback and item exposure, ultimately…

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…

Deep generative models are becoming widely used across science and industry for a variety of purposes. A common challenge is achieving a precise implicit or explicit representation of the data probability density. Recent proposals have…

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

A deep learning (DL) closure model for large-eddy simulation (LES) is developed and evaluated for incompressible flows around a rectangular cylinder at moderate Reynolds numbers. Near-wall flow simulation remains a central challenge in…