DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
Proposes a probabilistic model to improve hydrology predictions and trust.
problem Noisy or missing basin characteristics impact streamflow prediction.
method Probabilistic inverse modeling framework to reconstruct basin characteristics.
result 6% improvement in R2 for streamflow prediction, 17% reduction in uncertainty. Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purp…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for in…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for in…
Physics-informed deep learning for PDEs solves forward and inverse problems efficiently.
problem Solving forward and inverse problems in parametric PDEs efficiently and accurately.
method Physics-informed deep latent variable model (PDDLVM) combining deep neural networks, probabilistic modelling, and variational inference.
result Achieves up to three orders of magnitude speed-up compared to traditional FEM while providing coherent uncertainty estimates.
New method uses Gaussian ODE filtering to approximate likelihoods for fast ODE inverse problems.
problem Intractable forward models in likelihood-free inference, especially for ODEs.
method Gaussian ODE filtering to construct local Gaussian likelihood approximations.
result New solvers outperform standard likelihood-free approaches on benchmark systems.
Bayesian inference of discrete component states in civil infrastructures using PGMs and GNNs.
problem Inferring discrete states of civil infrastructure components from measurable responses is an ill-posed inverse problem.
method The study proposes a novel Bayesian inversion paradigm based on Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs). PGMs are used to model the problem, with parameters learned from data and structural topology prior. Inference is accomplished by GNNs, and a graph property-based training strategy is developed.
result The proposed framework effectively solves the challenges of inferring the posterior PDF for discrete variables in high-dimensional problems.
Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or su…
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.
New method finds all thin film structures from reflectometry data.
problem Computational prohibitive for standard algorithms, leading to unreliable analysis.
method Prior-Amortized Neural Posterior Estimation (PANPE) combining simulation-based inference and adaptive priors.
result Identifies all realistic structures in seconds, setting new standards in reflectometry.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
Probabilistic inversion within a multiple-point statistics framework is often computationally prohibitive for high-dimensional problems. To partly address this, we introduce and evaluate a new training-image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generat…
Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with task dimensionality, an…
Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.
problem Understanding the inverse problem of inferring cost matrices from optimal couplings.
method Formalized and analyzed using entropy-regularized optimal transport, with theoretical and empirical contributions.
result Characterization of the manifold of cross-ratio equivalent costs and derivation of an MCMC sampler.
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.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
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.
Study uses DNNs for real-time EM inversion, highlighting model errors and proposing solutions.
problem Model errors in DNNs affect real-time geosteering decisions in EM measurements.
method Bayesian ensemble smoothing with DNNs for thousands of model evaluations, identifying multimodality.
result Model errors can lead to biased estimates, necessitating error reduction techniques.
A deep learning approach solves probabilistic inverse problems with physical constraints.
problem Solving inverse problems with large inferred vectors and prior samples.
method Uses conditional Wasserstein generative adversarial networks (cWGAN) with full gradient penalty.
result Improves accuracy and robustness in sampling and solving inverse problems.
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.
Paper presents a new video generation model using diffusion probabilistic methods.
problem Generating high-quality video sequences.
method Denoising diffusion probabilistic models, autoregressive, end-to-end optimization.
result Significant improvements in perceptual quality and probabilistic frame forecasting.
MDNs offer a data-efficient alternative to diffusion and flow models for multimodal scientific learning.
problem Capturing multimodal conditional uncertainty in scientific inverse problems.
method Mixture Density Networks (MDNs) as explicit parametric density estimators.
result MDNs achieve superior generalization, interpretability, and sample efficiency in scientific tasks.
This is mainly a survey, explaining how the probabilistic (statistical mechanical) construction of Kahler-Einstein metrics on compact complex manifolds, introduced in a series of works by the author, naturally arises from classical approximation and interpolation problems in complex n-space. A fair amount of background…
This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems Bx=b with positive definite B for x. The goal is to replace the point estimates returned by existing methods with a Gaussian posterior belief over the elements of the inverse of B, which can …
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming majority of pertinent methods is based on the assumption of a perfect model. Motiva…
Autonomous vehicles (AVs) are on the road. To safely and efficiently interact with other road participants, AVs have to accurately predict the behavior of surrounding vehicles and plan accordingly. Such prediction should be probabilistic, to address the uncertainties in human behavior. Such prediction should also be in…
New methods tackle statistical inverse problems with random data.
problem Statistical inverse problems with random experimental design.
method Spectral regularization, regularization by projection, convex penalties.
result Minimax rates in expectation and probability for convergence.
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.
New method uses CNN for seismic inversion uncertainty quantification.
problem Uncertainty quantification in seismic inversion for noisy data.
method Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) with CNN denoiser.
result High-resolution, trustworthy posterior samples for subsurface structures.
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
New method infers human sensorimotor costs from behavior.
problem Inferring human sensorimotor costs from observed behavior.
method Inverse optimal control with signal-dependent noise.
result Recovering costs and benefits in sensorimotor behavior.
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.
The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, g…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional latent scenes, due to challenges in both modeling and inference. Accounting for th…
Generative model for morphisms in free categories learns from wiring diagrams.
problem Learning and generating morphisms in free monoidal categories.
method Probabilistic generative model using variational inference and maximum likelihood.
result The model achieves competitive performance on the Omniglot dataset.
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.
Kernel estimator optimally recovers function from noisy exponential Radon transform.
problem Inverting noisy exponential Radon transform of a function.
method Proposed a kernel estimator to estimate the true function.
result The estimator converges to the true function at minimax optimal rate.
Using a probabilistic argument we show that the second bounded cohomology of an acylindrically hyperbolic group G (e.g., a non-elementary hyperbolic or relatively hyperbolic group, non-exceptional mapping class group, Out(Fn), \dots) embeds via the natural restriction maps into the inverse limit of the secon…
A framework detects where constitutive models fail in elastography, improving clinical interpretation.
problem Assuming constitutive models correctly describe soft tissue mechanics leads to misleading results.
method Probabilistic framework treating stress as a latent variable, comparing it to assumed model predictions.
result Inferred precision field identifies invalid regions with high accuracy, improving model validity.
New method reduces memory usage for Bayesian inverse problems on large grids.
problem Solving large-scale linear inverse problems with Gaussian process priors.
method Implicit representation of posterior covariance matrices, sequential disintegrations of Gaussian measures.
result Significant reduction in uncertainty for high-density regions estimation.
New algorithms speed up inverse reinforcement learning by solving MDPs once.
problem Slow convergence in Maximum Entropy Inverse Reinforcement Learning.
method Deep Inverse Q-learning with constraints exploiting Q-learning.
result Up to several orders of magnitude speedup compared to existing methods.
Unified derivation of diffusion models using PDEs for inverse problems.
problem Solving inverse problems in physics-based applications.
method Deriving diffusion models using PDEs for a unified approach.
result Unified derivation and new class of variance preserving models.
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple …
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
Providing a suitable reward function to reinforcement learning can be difficult in many real world applications. While inverse reinforcement learning (IRL) holds promise for automatically learning reward functions from demonstrations, several major challenges remain. First, existing IRL methods learn reward functions f…
EASE estimator improves probabilistic value estimation efficiency.
problem Efficiently estimating probabilistic values like Shapley and semivalues.
method Developed an Efficiency-Aware Surrogate-adjusted Estimator (EASE) that minimizes first-order mean squared error.
result EASE consistently outperforms existing estimators for various probabilistic values.
Proposes a neural network for sparsity regularization in inverse problems using Gaussian mixture.
problem Sparsity in inverse problems with limited significant components.
method Probabilistic sparsity prior as a mixture of degenerate Gaussians, trained with neural network.
result Neural network yields lower mean square error than LASSO, group LASSO, and iterative hard thresholding.