Related papers: Coarse Graining with Neural Operators for Simulati…
Reduced-order models (ROMs) have become an essential tool for reducing the computational cost of fluid flow simulations. While standard ROMs can efficiently approximate laminar flows, their accuracy often suffers in convection-dominated…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…
Solving multi-objective optimization problems for large deep neural networks is a challenging task due to the complexity of the loss landscape and the expensive computational cost of training and evaluating models. Efficient Pareto front…
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Accurate and unambiguous guidelines are critical for large language model (LLM) based graders, yet manually crafting these prompts is often sub-optimal as LLMs can misinterpret expert guidelines or lack necessary domain specificity.…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…
Coarse graining techniques play an essential role in accelerating molecular simulations of systems with large length and time scales. Theoretically grounded bottom-up models are appealing due to their thermodynamic consistency with the…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
Numerical simulations play a critical role in design and development of engineering products and processes. Traditional computational methods, such as CFD, can provide accurate predictions but are computationally expensive, particularly for…
Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…
Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification in…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…