2 citations · 3 across the 18 of their papers we have counts for
13 papers · 1 filter
Learning Physics from an Imperfect Ancestor
S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas +1
Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependen…
ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
Rajyasri Roy, Dibyajyoti Nayak, Somdatta Goswami
Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitivel…
Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury
Anusha Agarwal, Dibakar Roy Sarkar, Somdatta Goswami
Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computati…
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…
Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference
Luis Mandl, Dibyajyoti Nayak, Tim Ricken +1
Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning.…
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)…
TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation
Dibyajyoti Nayak, Somdatta Goswami
Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conv…
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…
Learning Hidden Physics and System Parameters with Deep Operator Networks
Dibakar Roy Sarkar, Vijay Kag, Birupaksha Pal +1
Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data…
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…
Efficient Training of Deep Neural Operator Networks via Randomized Sampling
Sharmila Karumuri, Lori Graham-Brady, Somdatta Goswami
Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has…