Bayesian Deep Learning tackles inverse problems with neural networks and approximate computations.
problem Solving inverse problems with indirect measurements and uncertainties.
method Bayesian Deep Learning, using neural networks and approximate computations.
result Effective solutions for inverse problems using Bayesian Deep Learning.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Bayesian geoacoustic inversion improved using MDN.
problem Efficiently solving Bayesian geoacoustic inversion problems.
method Deriving geoacoustic statistics from multidimensional posterior density using MDN, training the network on the whole parameter space.
result The network provides reliable predictions and good generalization performance, solving problems in seconds.
Study uses machine learning to solve photoacoustic tomography's inverse problem.
problem Solving the full inverse problem in photoacoustic tomography.
method Developed an approach using variational autoencoders for Bayesian estimation of the posterior distribution.
result Evaluated the approach with numerical simulations and compared it to a Bayesian solution.
Novel method uses deep generative models for efficient Bayesian inverse problem solving.
problem Efficiently solving inverse problems with large, discrete fields and limited prior information.
method Bayesian inference with deep generative models in low-dimensional latent space.
result Accurate and reliable uncertainty estimates for large-scale inverse problems.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
MCGDiff uses SGM to guide SMC for solving ill-posed linear inverse problems.
problem Solving ill-posed linear inverse problems in Bayesian settings.
method Exploiting SGM structure, defining a sequence of intermediate problems, and using SMC methods.
result MCGDiff outperforms competing methods in Bayesian ill-posed inverse problems.
Paper uses RL and diffusion models to solve Bayesian inverse problems.
problem Bayesian inverse problems with latent biases.
method Relative Trajectory Balance (RTB) for RL, conditional diffusion models, off-policy backtracking exploration.
result RTB improves diffusion model posteriors for inverse problems.
New method uses diffusion models for Bayesian inverse problems.
problem Solving Bayesian inverse problems with linear-Gaussian models.
method Decoupled Diffusion Sequential Monte Carlo (DDSMC) method.
result Asymptotically exact solution demonstrated on various data types.
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most realistic imaging applications in the clinic. We introduce two novel deep learning bas…
SKT improves EKI for Bayesian inverse problems with non-Gaussian targets.
problem Efficiently solving Bayesian inverse problems with expensive forward models and non-Gaussian posterior distributions.
method Embedding EKI and FAKI within a Bayesian annealing scheme to adapt tpCN sampler.
result Significant improvements in convergence rate compared to standard SMC and pCN.
New algorithm speeds up Bayesian UQ for high-dimensional inverse problems.
problem Computational inefficiency in Bayesian inference for high-dimensional inverse problems.
method Deep neural network-based autoencoder for dimension reduction and emulation phase.
result Computational efficiency up to three orders of magnitude with scalable Bayesian UQ.
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties en…
Bayesian PINNs tackle uncertainty in inverse problems.
problem Uncertainty quantification in inverse problems.
method Hierarchical Bayesian formulation of PINNs with variational inference and Monte Carlo dropout.
result Quantification of uncertainties in reconstructed images.
Paper introduces variational inference for Bayesian inverse problems with gamma hyperpriors.
problem Bayesian inverse problems with sparse solutions.
method Variational iterative alternating scheme for hierarchical models with gamma hyperpriors.
result Accurate reconstruction and meaningful uncertainty quantification.
The paper solves IRL for Bayesian stopping time problems.
problem Identifying optimal actions in Bayesian stopping time problems.
method Novel IRL framework using Bayesian revealed preferences.
result Identifies optimality and constructs cost function estimates.
This study proposes an efficient surrogate for Darcy flow inverse problems.
problem Efficiently constructing accurate surrogate models for high-dimensional complex inverse problems.
method Sequential Bayesian design strategy to acquire a locally accurate surrogate model focusing on high-probability regions.
result The proposed method accelerates inversion accuracy and computational speed.
Unified Bayesian PINN framework for solving inverse problems in infrared image processing.
problem Solving inverse problems in high-dimensional settings with complex physics.
method Bayesian Physics-Informed Neural Networks (BPINN-IP) framework, incorporating physical laws and uncertainties.
result Unified framework for physical constraints, prior knowledge, and data-driven inference with uncertainty quantification.
Variational Gaussian Processes solve linear inverse problems efficiently.
problem Solving inverse problems where indirect observations are corrupted by noise.
method Variational Bayesian methods with Gaussian process priors and inducing variables.
result Posterior contraction rates can be attained by correctly tuned variational procedures.
A new machine learning method for Bayesian inverse problems in function spaces.
problem Bayesian inverse problems in function spaces with incompatibility of white noise sources.
method One-step generative transport with amortized neural operator and prior-aligned Gaussian random field.
result Generative operator trained on prior samples and noisy observations generates posterior samples efficiently.
A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.
problem Approximating posterior distributions in Bayesian inverse problems with intractable likelihoods.
method Proposes a mixture-based approximation of intermediate posterior distributions and uses Gibbs sampling for practical sampling.
result Validated the approach on image inverse problems and audio source separation, demonstrating improved performance.
A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of …
Paper addresses travel time tomography stability and statistical inversion.
problem Determining conformal factors of metrics from geodesic lengths.
method Established forward and inverse stability estimates; applied to Bayesian statistical inversion.
result Consistency of statistical inversion technique for travel time tomography.
New method solves high-dimensional Bayesian inverse problems efficiently.
problem Efficiently solving high-dimensional Bayesian inverse problems with limited data.
method Physics-informed Neural Operators with RealNVP architecture for invertibility and differentiability.
result Accurate approximations of the full posterior without additional forward solves or sampling.
Bayesian framework for image inversion using regularization by denoising.
problem Image inversion and regularization in imaging tasks.
method Bayesian approach with Langevin-within-split Gibbs sampling.
result Demonstrates the effectiveness of the proposed method through numerical experiments.
A new method tackles Bayesian inverse problems with complex PDEs.
problem Bayesian inverse problems with expensive forward model evaluations and high-dimensional priors.
method Domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method.
result The method efficiently solves Bayesian inverse problems in parallel and low-dimensional latent spaces.
Adaptive operator learning reduces costs in Bayesian inverse problems.
problem Reducing computational costs in Bayesian inverse problems governed by PDEs.
method Adaptive operator learning framework that gradually reduces modeling error.
result The approach significantly reduces computational costs while maintaining inversion accuracy.
NF-ULA combines Langevin Monte Carlo with normalizing flows for imaging inverse problems.
problem Solving inverse problems in imaging with uncertainty quantification.
method Langevin Monte Carlo with normalizing flow prior.
result NF-ULA outperforms competing methods for severely ill-posed inverse problems.
Bayesian inverse problems use generative models for efficient inference.
problem Efficiently solving inverse problems with limited data and expert knowledge.
method Generative models trained on databases, Laplace approximation for prior density.
result Bayes estimates are consistent, not dependent on generative model quality.
Bayesian framework learns prior from data to quantify uncertainty in MRI reconstruction.
problem Quantifying uncertainty in deep learning solutions for inverse problems.
method Adopting denoising score matching to learn prior from data, using it in an annealed Hamiltonian Monte-Carlo scheme.
result The approach yields high-quality reconstructions and assesses uncertainty on specific features.
Bayesian inference identifies model parameters from financial data to detect arbitrage opportunities.
problem Identifying model parameters from financial data to detect arbitrage opportunities.
method Bayesian inference approach using Markov Chain Monte Carlo (MCMC) algorithm.
result Bayesian inference can estimate unknown trend and volatility coefficients from measured data.
WNVI solves inverse problems without forward models using neural networks.
problem Solving high-dimensional Bayesian inverse problems based on PDEs.
method WNVI uses weighted residuals and SVI with neural networks to infer state variables and unknowns.
result WNVI is more accurate and efficient than traditional methods and handles ill-posed problems.
Bayesian method refines surrogate models for accurate full waveform inversion.
problem Complex input/output relations in full waveform inversion make accurate surrogate models difficult.
method Iterative refinement of surrogate models using MCMC samples and progressively expanding frequency bandwidth.
result Highly accurate surrogate model across full bandwidth enables accurate final MCMC inversion.
Bayesian ANN method predicts chaotic systems with uncertainty.
problem Estimating chaotic dynamical systems from noisy data.
method Bayesian Artificial Neural Networks for ODE inverse problems.
result Accurate time predictions and uncertainty bounds.
Gaussian process regression helps approximate Bayesian inverse problems efficiently.
problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2-norm error between true and approximate likelihood. Bayesian method estimates dynamics from near-optimal trajectories.
problem Estimating dynamics from near-optimal expert trajectories in reinforcement learning.
method Constraint-based Bayesian approach integrating expert near-optimality.
result Significant improvements in decision-making and transfer success.
Paper examines stability of Bayesian posterior measures using integral probability metrics.
problem Stability of Bayesian inference in large-scale inverse problems.
method New families of integral probability metrics for likelihood and prior perturbations.
result Constructs new stability results for Bayesian posterior measures.
New method uses EKI for efficient Bayesian inference in high-dimensional problems.
problem Efficient inference for high-dimensional posterior distributions in physics-informed neural networks.
method Ensemble Kalman Inversion (EKI) for high-dimensional posterior inference.
result EKI-based inference provides comparable uncertainty estimates to HMC-based methods but with reduced computational cost.
A new method maps high-dimensional Bayesian inverse problems to lower dimensions.
problem High-dimensional Bayesian inverse problems with complex prior information.
method Data-driven VAE prior and KRnet map for posterior approximation in latent space.
result Efficiently reduces computational cost and approximates posterior distributions.
LazyDINO efficiently solves high-dimensional Bayesian inverse problems with fast and scalable solutions.
problem High-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable maps.
method LazyDINO combines derivative-informed neural surrogates and lazy map variational inference for efficient posterior approximation.
result Significant cost reduction in amortized Bayesian inversion, achieving one to two orders of magnitude improvement.
Seismic inversion method uses GAN to improve efficiency and accuracy.
problem Difficulty in combining geological knowledge with seismic data and assessing uncertainty.
method Generative Adversarial Network (GAN) for seismic inversion.
result GAN-generated models conform to observation data with low uncertainty.
A new VAE approach solves inverse problems without explicit inverse mapping.
problem Solving inverse problems without explicit inverse mapping.
method Discarding the encoder in VAE architecture, directly optimizing latent variables.
result The latent variables can exhibit mutually independent properties without an encoding process.
Method solves Bayesian inverse problems in function space without assuming log-concavity.
problem Bayesian inverse problems in infinite-dimensional nonlinear settings.
method Score-based diffusion models as a prior, Langevin-type MCMC on function spaces.
result Provable convergence bound for posterior sampling, dependent on score approximation.
Bayesian approach improves rain field reconstruction using CMLs and DMs.
problem Challenges in accurately reconstructing ground-level rainfall from CML path-integrated measurements.
method Bayesian inverse problem with Diffusion Models as priors.
result Improved performance in rainfall estimation compared to existing methods.
Paper introduces a Gibbs sampler for Bayesian inversion of ill-posed problems.
problem Bayesian inversion of ill-posed problems with linear transformation and additive noise.
method Gibbs algorithm based on prior diffusion model.
result Gibbs algorithm offers a guarantee of convergence in a specific situation.
This paper revisits the Bayesian CMA-ES and provides updates for normal Wishart. It emphasizes the difference between a normal and normal inverse Wishart prior. After some computation, we prove that the only difference relies surprisingly in the expected covariance. We prove that the expected covariance should be lower…
Researchers use GANs to infer physics-based inverse problems, quantifying uncertainty and promoting generalizability.
problem Quantifying uncertainty in physics-based inverse problems.
method Trained conditional Wasserstein GANs with U-Net architecture and conditional instance normalization.
result The approach effectively samples from the posterior and promotes generalizability with out-of-distribution samples.
A new method uses DMs as priors for imaging problems, offering more accurate reconstructions.
problem Accurate probabilistic imaging for complex inverse problems.
method Markov chain Monte Carlo algorithm using DMs as plug-and-play priors for solving Bayesian inverse problems.
result Offers more accurate reconstructions and posterior estimation compared to existing methods.