Related papers: Data-driven learning of robust nonlocal physics fr…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…

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,…

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory informed neural network trained on kinetic Particle-in-Cell simulations that span both local and nonlocal regimes. The model…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…

We introduce the concept of decision-focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex,…

A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano- and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward…