Related papers: Incremental Neural Controlled Differential Equatio…

We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time…

A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate construction and is further used for uncertainty quantification and inverse modeling tasks. The framework is built based on the Auto-Encoder (or Encoder-Decoder)…

We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…

The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…

In recent years, various artificial intelligence-based surrogate models have been proposed to provide rapid manufacturability predictions of material forming processes. However, traditional AI-based surrogate models, typically built with…

The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic…

There is renewed interest in developing small modular reactors and micro-reactors. Innovation is necessary in both construction and operation methods of these reactors to be financially attractive. For operation, an area of interest is the…

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…