Related papers: A Physics-Informed Auto-Learning Framework for Dev…

Traditional energy-based learning models associate a single energy metric to each configuration of variables involved in the underlying optimization process. Such models associate the lowest energy state to the optimal configuration of…

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…

Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

We present a physics-informed Bayesian neural-network framework to infer neutron-star equations of state from theoretical priors and to propagate the associated uncertainties to stellar observables. Trained on a large and representative…

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings…

A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear…

We present a latent variable model for classification that provides a novel probabilistic interpretation of neural network softmax classifiers. We derive a variational objective to train the model, analogous to the evidence lower bound…

We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that…

We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…

Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility govern their behavior…

Auto-encoding Variational Bayes (AEVB) is a powerful and general algorithm for fitting latent variable models (a promising direction for unsupervised learning), and is well-known for training the Variational Auto-Encoder (VAE). In this…

Systems involving Partial Differential Equations (PDEs) have recently become more popular among the machine learning community. However prior methods usually treat infinite dimensional problems in finite dimensions with Reduced Order…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

Model-Based Reinforcement Learning distinguishes between physical dynamics models operating on proprioceptive inputs and latent dynamics models operating on high-dimensional image observations. A prominent latent approach is the Recurrent…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Global deep-learning weather prediction models have recently been shown to produce forecasts that rival those from physics-based models run at operational centers. It is unclear whether these models have encoded atmospheric dynamics, or…