Related papers: Dimensionality reduction can be used as a surrogat…
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…
Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a…
Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised…
Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are…
Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…
We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
We propose a class of very simple modifications of gradient descent and stochastic gradient descent. We show that when applied to a large variety of machine learning problems, ranging from logistic regression to deep neural nets, the…
Surrogate models - also called emulators - are widely used to facilitate Bayesian inference in settings where computational costs preclude the use of standard posterior inference algorithms. Their deployment is now standard practice across…
Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…
Surrogate model-based optimization has been increasingly used in the field of engineering design. It involves creating a surrogate model with objective functions or constraints based on the data obtained from simulations or real-world…
Microstructure evolution, which plays a critical role in determining materials properties, is commonly simulated by the high-fidelity but computationally expensive phase-field method. To address this, we approximate microstructure evolution…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for…
We develop a systematic approach for surrogate model construction in reduced input parameter spaces. A sparse set of model evaluations in the original input space is used to approximate derivative based global sensitivity measures (DGSMs)…
Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods…
The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional,…
We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by…
Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high…
We study consistency properties of machine learning methods based on minimizing convex surrogates. We extend the recent framework of Osokin et al. (2017) for the quantitative analysis of consistency properties to the case of inconsistent…