Related papers: Hierarchical Physics-Embedded Learning for Predict…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…

Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…

Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally…

Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…