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We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

Machine Learning · Statistics 2018-12-11 Yibo Yang , Paris Perdikaris

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

Soft Condensed Matter · Physics 2022-10-11 Kyle R. Lennon , Gareth H. McKinley , James W. Swan

This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and…

Numerical Analysis · Mathematics 2026-03-30 Animesh Biswas , Archie Huang , Shaurya Agarwal , Christopher Housholder

In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible physics-based…

Numerical Analysis · Mathematics 2023-02-01 I. B. C. M. Rocha , P. Kerfriden , F. P. van der Meer

Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in…

Machine Learning · Computer Science 2025-01-07 Ruiquan Huang , Yingbin Liang , Jing Yang

Machine learning (ML) techniques, especially neural networks (NNs), have shown promise in learning subgrid-scale parameterizations for climate models. However, a major problem with data-driven parameterizations, particularly those learned…

Atmospheric and Oceanic Physics · Physics 2024-07-17 Hamid A. Pahlavan , Pedram Hassanzadeh , M. Joan Alexander

The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…

Machine Learning · Statistics 2025-10-06 Libin Zhu , Damek Davis , Dmitriy Drusvyatskiy , Maryam Fazel

Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to…

Machine Learning · Computer Science 2025-07-21 Jiaxiang Yi , Bernardo P. Ferreira , Miguel A. Bessa

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to…

Robotics · Computer Science 2022-09-21 John Irvin Alora , Mattia Cenedese , Edward Schmerling , George Haller , Marco Pavone

A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…

Computational Engineering, Finance, and Science · Computer Science 2023-04-28 Kshitiz Upadhyay , Jan N. Fuhg , Nikolaos Bouklas , K. T. Ramesh

The typical approach for learned DBMS components is to capture the behavior by running a representative set of queries and use the observations to train a machine learning model. This workload-driven approach, however, has two major…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Dynamical Systems · Mathematics 2018-01-08 Maziar Raissi , Paris Perdikaris , George Em Karniadakis

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…

Machine Learning · Statistics 2025-07-22 Yuejie Chi , Yuxin Chen , Yuting Wei

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Machine Learning · Computer Science 2025-03-14 Jan-Hendrik Bastek , WaiChing Sun , Dennis M. Kochmann

Deep reinforcement learning (DRL) requires the collection of interventional data, which is sometimes expensive and even unethical in the real world, such as in the autonomous driving and the medical field. Offline reinforcement learning…

Machine Learning · Computer Science 2023-06-12 Wenxuan Zhu , Chao Yu , Qiang Zhang

In real world clinical environments, training and applying deep learning models on multi-modal medical imaging data often struggles with partially incomplete data. Standard approaches either discard missing samples, require imputation or…

Computer Vision and Pattern Recognition · Computer Science 2025-09-16 Christoph Fürböck , Paul Weiser , Branko Mitic , Philipp Seeböck , Thomas Helbich , Georg Langs

Data-driven neural networks are increasingly used as surrogate forward models in geophysics, but it remains unclear whether they recover only the data mapping or also the underlying physical sensitivity structure. Here we test this question…

Machine Learning · Computer Science 2026-04-07 Ziye Yu , Yuqi Cai , Xin Liu

Molecular dynamics (MD) simulations have become indispensable for exploring tribological deformation patterns at the atomic scale. However, transforming the resulting high-dimensional data into interpretable deformation pattern maps remains…

Materials Science · Physics 2025-12-08 Hendrik J. Ehrich , Marvin C. May , Stefan J. Eder

We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability…

Machine Learning · Computer Science 2020-02-25 Markus Schöberl , Nicholas Zabaras , Phaedon-Stelios Koutsourelakis

The design of data-driven formulations for machine learning and decision-making with good out-of-sample performance is a key challenge. The observation that good in-sample performance does not guarantee good out-of-sample performance is…

Machine Learning · Statistics 2025-02-04 Amine Bennouna , Bart Van Parys , Ryan Lucas
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