Related papers: Weak neural variational inference for solving Baye…
The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs…
In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good…
Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical…
Systems involving Partial Differential Equations (PDEs) have recently become more popular among the machine learning community. However prior methods usually treat infinite dimensional problems in finite dimensions with Reduced Order…
We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
Full-waveform inversion (FWI) is a widely used technique in seismic processing to produce high resolution Earth models that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise in a…
Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…
We introduce a new method for learning Bayesian neural networks, treating them as a stack of multivariate Bayesian linear regression models. The main idea is to infer the layerwise posterior exactly if we know the target outputs of each…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…