inverse-problems

The paper introduces a reference-free instrument to detect and discriminate operator misspecification in hybrid PDE-parameter learning from a single fit, demonstrating its effectiveness on a parabolic inverse problem while separating it from parameter unidentifiability.

A tweet promoting the book 'Deep Learning Methods Of Mathematical Physics - Volume I: Direct And Inverse Problems' by Ovidiu Calin, which explores AI and deep learning applications in mathematical physics.

An essay critiquing the common conflation of optimization and learning in neural network research, arguing that training should be understood as inverse reconstruction and studied through the evolving homology of weight-defined piecewise manifolds.

This article explores the difficulty of AI alignment from a mathematical perspective, pointing out that neural networks, through characteristics such as ill-posed inverse problem inference, attribute-less numerical computation, and full-rank transformations, make it difficult to clearly specify and accurately represent human values, thereby elucidating the mathematical essence of the alignment problem.

This paper introduces ImagingBench, a benchmark of 20 computational imaging tasks to evaluate agentic AI systems' ability to handle physics-based imaging problems, finding that current models, including Gemini, GPT, and Qwen, perform poorly compared to specialized methods.

This paper investigates out-of-distribution neural inference for reconstructing interaction graphs of dynamical Ising models, finding that Transformer-based and convolutional models exhibit architecture-dependent statistical priors that can produce misleading out-of-distribution robustness.

This paper investigates whether sentence embeddings can serve as an inference-time interface for injecting geological knowledge into a learned Darcy-flow inverse solver, finding that text conditioning reduces reconstruction error by 81% relative to a no-text counterfactual, with most gains from categorical class-level constraints.

This paper introduces the degeneracy distillery, a method that automatically detects and resolves degenerate parameter combinations in physical models by estimating and flattening the Fisher information matrix, reducing the simulation budget required for neural posterior estimation while providing physical insight.

This thread discusses the concept of 'Jagged Intelligence' in AI, framing it as a consequence of AI learning being an ill-posed inverse problem, and argues that external stabilizers like scaffolding and verification are essential.

Introduces Decoupled Latent Optimization (DLO) for full waveform inversion, which relaxes latent optimization into a quadratic-penalty objective, outperforming classical and diffusion-based methods on benchmarks while preserving smoothed-velocity initialization.

This paper proposes a history-bootstrapped autoregressive flow matching method for reconstructing full spatiotemporal fields (velocity and temperature) from partial observations of boiling dynamics, addressing the ill-posed inverse problem with non-Markovian posterior.

Proposes a variance-reduced zeroth-order Langevin sampling method for non-log-concave distributions, establishing the first non-asymptotic convergence guarantees, and applies it to inverse problems with score-based generative priors.

Proposes a hierarchical variational policy framework for reward-guided diffusion, enabling high-quality sampling with reduced inference cost. Achieves strong quality-speed tradeoff on tasks like super-resolution.

A comprehensive survey reviewing recent advances in using artificial intelligence to solve inverse partial differential equation (PDE) problems, covering inverse problems, inverse design, and control problems, with applications across scientific and industrial domains.

This paper introduces a new energy-based model for linear inverse problems that learns normalized posterior densities, overcoming limitations of diffusion models. It enables unbiased sampling, adaptive sampling, and blind degradation estimation, with competitive performance on ImageNet, CelebA, and AFHQ.

Steven Brunton announces his new book 'Optimization: A Bootcamp for Machine Learning, Inverse Problems, and Control', with pre-order available and accompanying free PDF, YouTube videos, and Python code.

This paper proposes NeTMY, an amortization-free coordinate neural field for inverse problems in NV-center quantum sensing, using a corrected forward model and sparse reconstruction losses to overcome center-collapse pathologies.

This paper presents a Bayesian inverse problem framework for rain field reconstruction using Commercial Microwave Links and Diffusion Model priors, demonstrating improved accuracy over existing baselines.

This paper analyzes zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, providing information-theoretic guarantees and proposing a projected-Langevin initialization method.