Related papers: Predicting and explaining nonlinear material respo…

Dislocation mobility, which dictates the response of dislocations to an applied stress, is a fundamental property of crystalline materials that governs the evolution of plastic deformation. Traditional approaches for deriving mobility laws…

Deep neural networks (DNN) have been used successfully in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. In this paper, we…

Inductive bias is a key factor in spatial regression models, determining how well a model can learn from limited data and capture spatial patterns. This work revisits the inductive biases in Geographically Neural Network Weighted Regression…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…

To advance the transparency of learning machines such as Deep Neural Networks (DNNs), the field of Explainable AI (XAI) was established to provide interpretations of DNNs' predictions. While different explanation techniques exist, a popular…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior.…

We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too…

An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…

While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the…

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…

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…

This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-dimensional singularly perturbed boundary value problems…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Deep learning has revolutionized modern society but faces growing energy and latency constraints. Deep physical neural networks (PNNs) are interconnected computing systems that directly exploit analog dynamics for energy-efficient,…

Neural networks (NNs) accelerate simulations of quantum dissipative dynamics. Ensuring that these simulations adhere to fundamental physical laws is crucial, but has been largely ignored in the state-of-the-art NN approaches. We show that…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

We investigate the construction of generative models capable of encoding physical constraints that can be hard to express explicitly. For the problem of inverse material design, where one seeks to design a material with a prescribed set of…