Related papers: Coarse Graining with Neural Operators for Simulati…
Despite tremendous progress in developing deep-learning-based weather forecasting systems, their design space, including the impact of different design choices, is yet to be well understood. This paper aims to fill this knowledge gap by…
Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…
The spread of machine learning techniques coupled with the availability of high-quality experimental and numerical data has significantly advanced numerous applications in fluid mechanics. Notable among these are the development of data…
Deterministic closures for coarse-grained turbulence models help reproduce mean statistics, but often fail to capture the finite-time growth of uncertainty. Using the framework of shell models as a quantitative multi-scale testbed, we…
Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized…
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed,…
In this paper we focus on the development of new methods suitable for efficient and reliable coarse-graining of {\it non-equilibrium} molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction…
Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…
Training machine learning (ML) algorithms is a computationally intensive process, which is frequently memory-bound due to repeatedly accessing large training datasets. As a result, processor-centric systems (e.g., CPU, GPU) suffer from…
This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…
Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…
This study proposes coarse-to-fine spatial modeling (CFSM) as a scalable and machine learning-compatible alternative to conventional spatial process models. Unlike conventional covariance-based spatial models, CFSM represents spatial…
Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…
Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…
Autonomous driving involves complex tasks such as data fusion, object and lane detection, behavior prediction, and path planning. As opposed to the modular approach which dedicates individual subsystems to tackle each of those tasks, the…
We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…