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Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Time series modeling, a crucial area in science, often encounters challenges when training Machine Learning (ML) models like Recurrent Neural Networks (RNNs) using the conventional mini-batch training strategy that assumes independent and…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

We proposed the molecular hyper-message passing network (MolHMPN) that predicts the properties of a molecule with prior knowledge-guided subgraph. Modeling higher-order connectivities in molecules is necessary as changes in both the…

Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to…

Fast and accurate treatment of collisions in the context of modern N-body planet formation simulations remains a challenging task due to inherently complex collision processes. We aim to tackle this problem with machine learning (ML), in…

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This…

In this study, we tackle the challenging task of predicting secondary structures from protein primary sequences, a pivotal initial stride towards predicting tertiary structures, while yielding crucial insights into protein activity,…

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…

Message Passing Neural Networks (MPNNs) hold a key position in machine learning on graphs, but they struggle with unintended behaviors, such as over-smoothing and over-squashing, due to irregular data structures. The observation and…

Fourier ptychography (FP) is a newly developed computational imaging approach that achieves both high resolution and wide field of view by stitching a series of low-resolution images captured under angle-varied illumination. So far, many…

Machine Learning methods and, in particular, Artificial Neural Networks (ANNs) have demonstrated promising capabilities in material constitutive modeling. One of the main drawbacks of such approaches is the lack of a rigorous frame based on…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

Modeling plays a critical role in additive manufacturing (AM), enabling a deeper understanding of underlying processes. Parametric solutions for such models are of great importance, enabling the optimization of production processes and…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph…