Related papers: Tau-BNO: Brain Neural Operator for Tau Transport M…

Mathematical modeling offers a valuable approach to understanding Alzheimers disease (AD) given its complexity, unknown causes, and lack of effective treatments. Models, once validated, offer a powerful tool to test medical hypotheses that…

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…

Emerging neuroimaging evidence shows that pathological tau proteins build up along specific brain networks, suggesting that large-scale network architecture plays a key role in the progression of Alzheimer's disease (AD). However, how…

Partial differential equations (PDEs) are widely used to model complex physical systems, but solving them efficiently remains a significant challenge. Recently, Transformers have emerged as the preferred architecture for PDEs due to their…

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric…

Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this…

Classical neural networks are known for their ability to approximate mappings between finite-dimensional spaces, but they fall short in capturing complex operator dynamics across infinite-dimensional function spaces. Neural operators, in…

Agent-based modeling (ABM) is a powerful computational approach for studying complex biological and biomedical systems, yet its widespread use remains limited by significant computational demands. As models become increasingly…

Agent-based modelling (ABM) is a widespread approach to simulate complex systems. Advancements in computational processing and storage have facilitated the adoption of ABMs across many fields; however, ABMs face challenges that limit their…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Bayesian optimization (BO), which uses a Gaussian process (GP) as a surrogate to model its objective function, is popular for black-box optimization. However, due to the limitations of GPs, BO underperforms in some problems such as those…

Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale…

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…

Transfer learning enhances the training of novel sensory and decision models by employing rich feature representations from large, pre-trained teacher models. Cognitive neuroscience shows that the human brain creates low-dimensional,…

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…

In scientific machine learning (SciML), a key challenge is learning unknown, evolving physical processes and making predictions across spatio-temporal scales. For example, in real-world manufacturing problems like additive manufacturing,…

We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…

Neural-network-based dynamics models learned from observational data have shown strong predictive capabilities for scene dynamics in robotic manipulation tasks. However, their inherent non-linearity presents significant challenges for…

This paper focuses on the feasibility of Deep Neural Operator (DeepONet) as a robust surrogate modeling method within the context of digital twin (DT) for nuclear energy systems. Through benchmarking and evaluation, this study showcases the…