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Patient-specific cardiac computational models are essential for the efficient realization of precision medicine and in-silico clinical trials using digital twins. Cardiac digital twins can provide non-invasive characterizations of cardiac…

Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can…

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional…

Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains under-explored. Learning…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in…

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically,…

During the curing process of composites, the temperature history heavily determines the evolutions of the field of degree of cure as well as the residual stress, which will further influence the mechanical properties of composite, thus it…

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

There has recently been increasing attention towards developing foundational neural Partial Differential Equation (PDE) solvers and neural operators through large-scale pretraining. However, unlike vision and language models that make use…

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current…

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…