Related papers: Calibrated Physics-Informed Uncertainty Quantifica…
Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As…
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…
Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability…
Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…
Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…
Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…
Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…
Development of an accurate, flexible, and numerically efficient uncertainty quantification (UQ) method is one of fundamental challenges in machine learning. Previously, a UQ method called DISCO Nets has been proposed (Bouchacourt et al.,…
Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents…
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel…
We propose a physics-informed quantum algorithm to solve nonlinear and multidimensional differential equations (DEs) in a quantum latent space. We suggest a strategy for building quantum models as state overlaps, where exponentially large…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
Recent advances in generative video models have led to significant breakthroughs in high-fidelity video synthesis, specifically in controllable video generation where the generated video is conditioned on text and action inputs, e.g., in…
We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…
We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN),…