Related papers: Probabilistic Deep Learning for Real-Time Large De…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are…

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…

We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…

Emerging deep-learning (DL)-based techniques have significant potential to revolutionize biomedical imaging. However, one outstanding challenge is the lack of reliability assessment in the DL predictions, whose errors are commonly revealed…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based…

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

We present a novel machine learning based surrogate modeling method for predicting spatially resolved 3D microstructure evolution of polycrystalline materials under uniaxial tensile loading. Our approach is orders of magnitude faster than…

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support…

Manipulation of elastoplastic objects like dough often involves topological changes such as splitting and merging. The ability to accurately predict these topological changes that a specific action might incur is critical for planning…

We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

We consider the point evaluation of the solution to interface problems with geometric uncertainties, where the uncertainty in the obstacle is described by a high-dimensional parameter $\boldsymbol{y}\in[-1,1]^d$, $d\in\mathbb{N}$. We focus…

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…

Natural disasters can have catastrophic impacts on the functionality of infrastructure systems and cause severe physical and socio-economic losses. Given budget constraints, it is crucial to optimize decisions regarding mitigation,…

The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…

Learning controller parameters from closed-loop data has been shown to improve closed-loop performance. Bayesian optimization, a widely used black-box and sample-efficient learning method, constructs a probabilistic surrogate of the…

Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed…