Related papers: Constitutive Manifold Neural Networks
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
Recently, a new frontier in computing has emerged with physical neural networks(PNNs) harnessing intrinsic physical processes for learning. Here, we explore topological mechanical neural networks(TMNNs) inspired by the quantum spin Hall…
Homogenization is a technique commonly used in multiscale computational science and engineering for predicting collective response of heterogeneous materials and extracting effective mechanical properties. In this paper, a three-dimensional…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…
Traditionally, 1D models based on scaling laws have been used to parameterized convective heat transfer rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus to tackle the computational bottleneck of high-fidelity…
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the…
The self-consistent field (SCF) generation of the three-dimensional (3D) electron density distribution ($\rho$) represents a fundamental aspect of density functional theory (DFT) and related first-principles calculations, and how one can…
Accurately predicting adsorption properties in nanoporous materials using Deep Learning models remains a challenging task. This challenge becomes even more pronounced when attempting to generalize to structures that were not part of the…
This paper introduces Associative Compression Networks (ACNs), a new framework for variational autoencoding with neural networks. The system differs from existing variational autoencoders (VAEs) in that the prior distribution used to model…
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…
In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be…
Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to…
Probabilistic graphical models are a central tool in AI; however, they are generally not as expressive as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic models such as sum-product networks…
Tensorial neural networks (TNNs) combine the successes of multilinear algebra with those of deep learning to enable extremely efficient reduced-order models of high-dimensional problems. Here, I describe a deep neural network architecture…
Feature extraction - the ability to identify relevant properties of data - is a key factor underlying the success of deep learning. Yet, it has proved difficult to elucidate its nature within existing predictive theories, to the extent that…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge…
Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing…
In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points…
Recent findings show that deep convolutional neural networks (DCNNs) do not generalize well under partial occlusion. Inspired by the success of compositional models at classifying partially occluded objects, we propose to integrate…