Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification

• URL: http://arxiv.org/abs/2502.10280v1
• Date: Fri, 14 Feb 2025 16:37:21 GMT
• Title: Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification
• Authors: Pengyu Zhang, Connor Duffin, Alex Glyn-Davies, Arnaud Vadeboncoeur, Mark Girolami,
• Abstract summary: Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data. Existing deep-learning based SR methods require large datasets labeled and lack reliable uncertainty quantification (UQ) We propose a probabilistic SR framework that leverages the Statistical Finite Element Method and energy-based generative modeling.
• Score: 7.093444028715175
• License:
• Abstract: Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR methods, require large labeled datasets and lack reliable uncertainty quantification (UQ), limiting their applicability in real-world scenarios. To overcome these challenges, we propose a probabilistic SR framework that leverages the Statistical Finite Element Method and energy-based generative modeling. Our method enables efficient high-resolution predictions with inherent UQ, while eliminating the need for extensive labeled datasets. The method is validated on a 2D Poisson example and compared with bicubic interpolation upscaling. Results demonstrate a computational speed-up over high-resolution numerical solvers while providing reliable uncertainty estimates.

Related papers

• Uncertainty separation via ensemble quantile regression [23.667247644930708]
  This paper introduces a novel and scalable framework for uncertainty estimation and separation. Our framework is scalable to large datasets and demonstrates superior performance on synthetic benchmarks.
  arXiv  Detail & Related papers  (2024-12-18T11:15:32Z)
• Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation for Time Series [45.76310830281876]
  We propose Quantile Sub-Ensembles, a novel method to estimate uncertainty with ensemble of quantile-regression-based task networks. Our method not only produces accurate imputations that is robust to high missing rates, but also is computationally efficient due to the fast training of its non-generative model.
  arXiv  Detail & Related papers  (2023-12-03T05:52:30Z)
• Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations [5.883258964010963]
  We study uncertainty quantification (UQ) for a class of deep learning-based BSDE schemes. We develop a UQ model that efficiently estimates the STD of the approximate solution using only a single run of the algorithm. Our numerical experiments show that the UQ model produces reliable estimates of the mean and STD of the approximate solution.
  arXiv  Detail & Related papers  (2023-10-05T09:00:48Z)
• PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data [11.15523311079383]
  PSRFlow is a novel normalizing flow-based generative model for scientific data super-resolution. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods.
  arXiv  Detail & Related papers  (2023-08-08T22:10:29Z)
• Validation Diagnostics for SBI algorithms based on Normalizing Flows [55.41644538483948]
  This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. This work should help the design of better specified models or drive the development of novel SBI-algorithms.
  arXiv  Detail & Related papers  (2022-11-17T15:48:06Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• FEM-based Real-Time Simulations of Large Deformations with Probabilistic Deep Learning [1.2617078020344616]
  We propose a highly efficient deep-learning surrogate framework that is able to predict the response of hyper-elastic bodies under load. The framework takes the form of special convolutional neural network architecture, so-called U-Net, which is trained with force-displacement data.
  arXiv  Detail & Related papers  (2021-11-02T20:05:22Z)
• Adaptive Anomaly Detection for Internet of Things in Hierarchical Edge Computing: A Contextual-Bandit Approach [81.5261621619557]
  We propose an adaptive anomaly detection scheme with hierarchical edge computing (HEC) We first construct multiple anomaly detection DNN models with increasing complexity, and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network.
  arXiv  Detail & Related papers  (2021-08-09T08:45:47Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization [85.84019017587477]
  Distributionally robust supervised learning is emerging as a key paradigm for building reliable machine learning systems for real-world applications. Existing algorithms for solving Wasserstein DRSL involve solving complex subproblems or fail to make use of gradients. We revisit Wasserstein DRSL through the lens of min-max optimization and derive scalable and efficiently implementable extra-gradient algorithms.
  arXiv  Detail & Related papers  (2021-04-27T16:56:09Z)
• Uncertainty-aware Remaining Useful Life predictor [57.74855412811814]
  Remaining Useful Life (RUL) estimation is the problem of inferring how long a certain industrial asset can be expected to operate. In this work, we consider Deep Gaussian Processes (DGPs) as possible solutions to the aforementioned limitations. The performance of the algorithms is evaluated on the N-CMAPSS dataset from NASA for aircraft engines.
  arXiv  Detail & Related papers  (2021-04-08T08:50:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.