Related papers: Latent Space Element Method
Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…
Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a…
During the design process of an autonomous underwater vehicle (AUV), the pressure vessel has a critical role. The pressure vessel contains dry electronics, power sources, and other sensors that can not be flooded. A traditional design…
In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…
Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
Simulations of optical quantum systems are essential for the development of quantum technologies. However, these simulations are often computationally intensive, especially when repeated evaluations are required for data fitting, parameter…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…
A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods…
Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…
Artificial intelligence is transforming scientific computing with deep neural network surrogates that approximate solutions to partial differential equations (PDEs). Traditional off-line training methods face issues with storage and I/O…
Physical based simulations can be very time and computationally demanding tasks. One way of accelerating these processes is by making use of data-driven surrogate models that learn from existing simulations. Ensembling methods are…
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a…
The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical…
This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…
In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the…
Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…