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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…

Machine Learning · Computer Science 2026-04-14 Minxing Zheng , Zewei Deng , Liyan Xie , Shixiang Zhu

We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a…

Computational Engineering, Finance, and Science · Computer Science 2026-05-25 Hagen Holthusen , Paul Steinmann , Ellen Kuhl

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…

We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic…

Numerical Analysis · Mathematics 2025-05-07 Kaushik Bhattacharya , Lianghao Cao , George Stepaniants , Andrew Stuart , Margaret Trautner

We study the problem of learning physical object representations for robot manipulation. Understanding object physics is critical for successful object manipulation, but also challenging because physical object properties can rarely be…

Robotics · Computer Science 2019-06-13 Zhenjia Xu , Jiajun Wu , Andy Zeng , Joshua B. Tenenbaum , Shuran Song

We assess the performance of EUCLID, Efficient Unsupervised Constitutive Law Identification and Discovery, a recently proposed framework for automated discovery of constitutive laws, on experimental data. Mechanical tests are performed on…

We introduce a data-driven framework for identifying material behavior from full-field kinematics and force measurements in generalized (micromorphic) continua. Unlike traditional approaches that rely on constitutive assumptions or…

Numerical Analysis · Mathematics 2025-12-18 Jacinto Ulloa , Laurent Stainier

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive…

Machine Learning · Computer Science 2022-04-04 Huaiqian You , Quinn Zhang , Colton J. Ross , Chung-Hao Lee , Ming-Chen Hsu , Yue Yu

Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…

Materials Science · Physics 2026-05-28 Reese E. Jones , Jan N. Fuhg

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…

Numerical Analysis · Mathematics 2020-06-24 Daniel Z. Huang , Kailai Xu , Charbel Farhat , Eric Darve

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…

Neural and Evolutionary Computing · Computer Science 2021-11-22 Gabriel Kronberger , Evgeniya Kabliman , Johannes Kronsteiner , Michael Kommenda

Materials and machines are often designed with particular goals in mind, so that they exhibit desired responses to given forces or constraints. Here we explore an alternative approach, namely physical coupled learning. In this paradigm, the…

Soft Condensed Matter · Physics 2021-09-07 Menachem Stern , Daniel Hexner , Jason W. Rocks , Andrea J. Liu

Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening…

Numerical Analysis · Mathematics 2024-03-11 Aleksandr Dekhovich , O. Taylan Turan , Jiaxiang Yi , Miguel A. Bessa

Goal: A limitation in robotic surgery is the lack of force feedback, due to challenges in suitable sensing techniques. To enhance the perception of the surgeons and precise force rendering, estimation of these forces along with tissue…

Systems and Control · Electrical Eng. & Systems 2025-04-30 Srikar Annamraju , Yuxi Chen , Jooyoung Lim , Inki Kim

A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…

Soft Condensed Matter · Physics 2020-07-06 Michael R. Buche , Meredith N. Silberstein

Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show,…

Disordered Systems and Neural Networks · Physics 2020-01-31 Henri Salmenjoki , Mikko J. Alava , Lasse Laurson

We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…

Machine Learning · Computer Science 2019-04-11 Ramakrishna Tipireddy , Paris Perdikaris , Panos Stinis , Alexandre Tartakovsky

Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like…

Robotics · Computer Science 2023-10-19 Bibit Bianchini , Mathew Halm , Michael Posa

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a…

Computational Engineering, Finance, and Science · Computer Science 2019-06-20 Laurent Stainier , Adrien Leygue , Michael Ortiz

The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art…

Machine Learning · Computer Science 2024-08-16 Kévin Garanger , Julie Kraus , Julian J. Rimoli
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