6 papers
Data-Efficient Time-Dependent PDE Surrogates: Graph Neural Simulators vs. Neural Operators
Dibyajyoti Nayak, Somdatta Goswami
Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional functio…
Enhanced accuracy through ensembling of randomly initialized auto-regressive models for time-dependent PDEs
Ishan Khurjekar, Indrashish Saha, Lori Graham-Brady +1
Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML)…
Enabling Local Neural Operators to perform Equation-Free System-Level Analysis
Gianluca Fabiani, Hannes Vandecasteele, Somdatta Goswami +2
Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly lear…
Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling
Wei Wang, Maryam Hakimzadeh, Haihui Ruan +1
Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way t…
Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs
Sharmila Karumuri, Lori Graham-Brady, Somdatta Goswami
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between…
Basis-to-Basis Operator Learning Using Function Encoders
Tyler Ingebrand, Adam J. Thorpe, Somdatta Goswami +2
We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We d…