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.
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.
Deep neural networks solve noisy, complex problems accurately.
problem Reconstructing solutions from noisy, high-dimensional, non-linear inverse problems.
method Restricting infinite-dimensional forward operators to finite-dimensional spaces, training neural networks to approximate these operators robustly to noise.
result Deep neural networks can accurately solve high-dimensional, noisy, non-linear inverse problems.
CNNs solve inverse problems during training, proving mutual coherence crucial for convergence.
problem Validation of CNN learning during training.
method Proved CNN elements solve inverse problems, discussed mutual coherence, and set training rules.
result Mutual coherence is necessary for CNNs to converge to optimum solutions.
Neumann networks solve inverse problems using truncated Neumann series.
problem Solving ill-posed linear inverse problems in imaging.
method Data-driven approach inspired by Neumann series, truncating the series to solve the problem directly.
result Trained Neumann networks outperform traditional methods and deep learning approaches.
ANNs solve complex inverse kinematics of a Tricept parallel robot.
problem Solving inverse kinematics for a Tricept parallel robot.
method Developed kinematic equations, used ANNs (MLP and RBF) for solving.
result ANNs provided proper accuracy and speed in solving complex inverse kinematics.
Convolutional neural networks can regularize inverse problems without training.
problem Solving inverse problems like image recovery from limited data.
method Fixed or parameterized convolutional networks with few parameters.
result Untrained convolutional networks can recover images from few measurements.
CNN outperforms other methods in gravity inversion.
problem Estimating subsurface density from gravitational field data.
method CNN, VAEs, GANs, iterative solvers (GD, GMRES, LGMRES, ICG).
result CNN provides the most reliable reconstructions.
The paper explores deep image priors for solving inverse problems.
problem Solving ill-posed inverse problems in image processing.
method Introduces and analyzes deep image priors as optimization of Tikhonov functionals.
result Analytic results for specific network designs and linear operators.
Improves inverse uncertainty quantification for time-dependent data using PCA and deep neural networks.
problem Efficiently quantify model input uncertainties from time-dependent experimental data.
method Functional PCA for dimensionality reduction, deep neural networks for surrogate modeling, Bayesian neural networks for uncertainty estimation.
result The proposed method reduces the computational cost and improves the agreement with experimental data.
Seismic inversion improved using semi-supervised sequence modeling.
problem Lack of geophysical constraints in machine learning seismic inversion.
method Semi-supervised sequence modeling with recurrent neural networks.
result Achieved 98% correlation between estimated and target elastic impedance.
Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying data-driven approaches to inverse problems, using a neural network as a regular…
Deep neural network solves complex groundwater contaminant source identification.
problem Identifying groundwater contaminant sources in highly heterogeneous media.
method Deep autoregressive neural network surrogate for forward model, ILUES for inversion.
result Deep autoregressive neural network provides accurate approximation for high-dimensional model.
Proposes a constant memory iterative inverse model using invertible networks.
problem Memory limitations in iterative learning approaches for inverse problems.
method Invertible networks to avoid storing intermediate activations, constant memory model.
result Trains 400-layer models on 3D MRI volumes, achieving state-of-the-art image reconstruction.
New method designs multilayer nanoparticles using AI.
problem Difficult to design multilayer nanoparticles by trial and error.
method Combines genetic algorithm and neural network for inverse design.
result Successfully designs multilayer nanoparticles efficiently.
INNs solve ambiguous inverse problems by learning forward and inverse processes together.
problem Determining hidden system parameters from ambiguous measurements.
method Invertible Neural Networks (INNs) learn both forward and inverse processes.
result INNs provide a full distribution over parameter space given a measurement and latent variables.
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.
Study of learning-based inverse problems using GANs.
problem Solving inverse problems with learned priors.
method Developed a simple non-convex algorithm for certain GAN architectures.
result The approach achieves linear convergence guarantees and improves upon conventional techniques.
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…
New algorithms solve inverse problems using deep learning, converging faster than traditional methods.
problem Solving inverse problems with deep learning models.
method Simple non-convex algorithm for linear and nonlinear inverse problems, with theoretical and empirical support.
result The proposed algorithms converge faster than conventional techniques for certain inverse problems.
Deep learning improves solving inverse problems with new generalization bounds and efficient regularization.
problem Solving inverse problems in various domains like medical imaging and remote sensing.
method Use of deep learning approaches with new generalization bounds and computationally efficient regularization strategies.
result Deep networks regularized with proposed strategies outperform standard approaches in image super-resolution tasks.
Injectivity of ReLU networks is characterized for generative models and inverse problems.
problem Injectivity in ReLU networks for generative models and inverse problems.
method Layerwise analysis, worst-case Lipschitz constants, differential topology, random projections.
result Global injectivity of ReLU networks requires expansivity between 3.4 and 10.5 for Gaussian matrices.
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
Study uses neural fields to improve geophysical inversions by reducing artifacts.
problem Improving geophysical inversions by reducing artifacts and improving model recovery.
method Employing neural fields for test-time learning in geophysical inversions.
result Test-time learning with neural fields eliminates unwanted artifacts in recovered models.
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.
Improves key instance detection in MIL models by using neural network inversion with sparseness constraint.
problem Limited key instance detection performance in attention-based deep MIL models due to skewed attention scores.
method Sparse network inversion with a sparseness constraint incorporated into neural network inversion, solved by proximal gradient method.
result Significantly improved key instance detection performance while maintaining bag-level prediction performance.
New method can infer training data from deep neural networks with high success rates.
problem Model inversion attacks on deep neural networks pose privacy risks.
method Generative model-inversion attack using GANs and partial public information.
result Significant improvement in identifying private training data from deep models.
Improves deep learning performance on noisy datasets using inverse-variance weighting.
problem Heteroscedastic regression with varying noise levels.
method Batch Inverse-Variance (BIV) loss function for neural networks.
result Significantly improves network performance on noisy datasets compared to other methods.
We show, analytically and numerically, that wealth distribution in the Bouchaud-Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.
Convolutional neural network improves MRE image reconstruction.
problem Reconstructing MRE images from displacement data is computationally intensive and costly.
method Proposes a CNN architecture to directly map MRE displacement data into elastograms, introducing a secondary loss for training.
result CNN-generated images compare favorably with nonlinear inversion methods.
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.
Paper solves inverse optimal transport problem with convex optimization and neural network.
problem Learning the cost function for optimal transport from observed data.
method Unconstrained convex optimization, Sinkhorn-Knopp algorithm, and deep neural network parameterization.
result Novel framework avoids repeated OT solving, demonstrating efficiency and accuracy.
Paper improves deep learning models for cardiac potential reconstruction.
problem Improving generalization of sequence models for cardiac potential reconstruction.
method Constrained stochasticity and global aggregation of temporal information in latent space.
result Improved generalization of inverse reconstruction networks.
Improved image recovery with minimal data using untrained neural networks.
problem Solving inverse problems with limited data.
method Pre-training neural networks with a small number of examples to improve performance.
result Performance increases as data increases, matching generative models with less than 1% of training data.
CNNs reconstruct medium properties from wave probing responses.
problem Determining medium properties from wave responses.
method Deep convolutional neural networks (CNNs) for nonlinear wave equations.
result Quantitative dependence of network depth and units on medium complexity.
Deep learning solves wave-based inverse problems, including super-resolution imaging.
problem Solving inverse wave scattering problems across all length scales.
method Wide-band butterfly network coupled with dynamic noise injection.
result Framework successfully solves super-resolution imaging problems.
Estimates input from output of nonlinear systems using ANN.
problem Estimating unknown compositional input from system output.
method Artificial Neural Networks (ANNs) for nonlinear system inversion.
result ANNs can compete with optimal bounds for linear systems and demonstrate promising results for nonlinear systems.
Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
Generative neural network designs novel 3D molecules with specified properties.
problem Designing molecules with desired properties in chemistry.
method Conditional generative neural network for 3D molecular structures.
result Demonstrated utility in generating novel molecules with specified motifs or composition.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
Improves deep network generalization for image sequence reconstruction.
problem Improving generalization of deep networks for inverse image reconstruction.
method Proposes a network optimized by a variational approximation of the information bottleneck principle with stochastic latent space.
result Demonstrates improved generalization ability of inverse reconstruction networks through stochasticity and information bottleneck.
A new method to understand neural networks by sampling the 'inverse set' of a neuron.
problem Understanding the internal representation of neurons in neural networks.
method Optimization-based sampling approach to characterize the input space that excites a neuron.
result Inspection of samples reveals regularities that help understand the neuron's representation.
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.
Represents neural networks as solutions to inverse problems in Banach spaces.
problem Understanding the function learned by neural networks.
method Variational framework, representer theorem, polynomial ridge splines.
result Neural networks are solutions to inverse problems in Banach spaces.
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…
Unified framework for lifted training and inversion of neural networks.
problem Challenges in gradient-based training of deep neural networks.
method Unified framework encapsulating various lifted training strategies.
result Unified framework improves training landscape and stability.
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.
Survey of deep learning methods for inverse problems, highlighting theoretical challenges.
problem Addressing theoretical gaps in deep learning for inverse problems.
method Survey of existing theoretical developments and open problems.
result Highlighting ongoing challenges in deep learning for inverse problems.