Related papers: Learning-based Multi-continuum Model for Multiscal…

In this work, we propose a novel model order reduction approach for two-phase flow in porous media by introducing a formulation in which the mobility, which realizes the coupling between phase saturations and phase pressures, is regarded as…

Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…

Denoising-based models, such as diffusion and flow matching, have been a critical component of robotic manipulation for their strong distribution-fitting and scaling capacity. Concurrently, several works have demonstrated that simple…

Multimodal learning aims to discover the relationship between multiple modalities. It has become an important research topic due to extensive multimodal applications such as cross-modal retrieval. This paper attempts to address the modality…

By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…

Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…

A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…

Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either…

In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum…

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…

We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectures developed for singularly perturbed forward problems, we…

In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multicontinuum homogenization, we introduce spatially smooth…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…