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Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…
Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Decision-making under uncertainty is often considered in two stages: predicting the unknown parameters, and then optimizing decisions based on predictions. While traditional prediction-focused learning (PFL) treats these two stages…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and understanding of first integrals are fundamental and important…
Using neural networks to solve partial differential equations (PDEs) is gaining popularity as an alternative approach in the scientific computing community. Neural networks can integrate different types of information into the loss…
Deploying reinforcement learning (RL) in safety-critical settings is constrained by brittleness under distribution shift. We study out-of-distribution (OOD) detection for RL time series and introduce DEEDEE, a two-statistic detector that…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…
Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…
In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…