2 citations · 3 across the 18 of their papers we have counts for
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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…
Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators
Dibakar Roy Sarkar, Ján Drgoňa, Somdatta Goswami
We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates time-integrated deep operator networks (TI-DeepONet) as differentiable…
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…