arXiv:2607. 21721v3 Announce Type: replace-cross Abstract: Where truths are scarce (e.
arXiv:2607. 21721v1 Announce Type: cross Abstract: Learned generative priors are increasingly used for ill-posed Bayesian inverse problems, their posterior uncertainty treated as earned from data.
arXiv:2606. 02309v1 Announce Type: new Abstract: Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions.
arXiv:2606. 04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty.
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
arXiv:2506. 20181v2 Announce Type: replace Abstract: We study operator relevance in data-driven partial differential equation (PDE) discovery.
The paper investigates why differentiable causal discovery methods that encode expert priors as forbidden-edge constraints via an Augmented Lagrangian (ALM) penalty—termed the "guide, not bind" approach—often fail. It identifies two key failures: (1) the sequential penalty‑ramping ALM suppresses a true edge before counterfactual checks can detect it, and the proposed adaptive relaxation rule DADU violates necessary conditions for safe relaxation, leading to a high failure rate across thousands of training runs; (2) the standard correlation‑matching objective inherently ties a true edge and its reverse to the same cost, whereas covariance matching can separate them by a provable margin. The authors provide theoretical propositions, corollaries, and empirical evidence to support these claims.
The paper presents a continually learning neural‑operator surrogate for the three‑dimensional forward operator used in time‑domain airborne electromagnetic (AEM) Bayesian inversion. By training on successive geological priors and employing an ensemble‑disagreement validity check, the surrogate replaces the expensive forward solver, enabling the Markov chain Monte Carlo sampler to reproduce the full‑solver posterior with credible intervals within 2.6 % of the truth. Applied to the 2013 Capricorn TEMPEST survey, the surrogate inverts over two million soundings in seconds, making uncertainty‑quantified conductivity imaging at survey scale feasible for near real‑time mineral‑systems targeting.
arXiv:2609.26272v1 Announce Type: new Abstract: Neural samplers are trained against an unnormalised target $\tilde\pi=e^{-E}$ with no samples from $\pi$, which leaves the practitioner with no way to...
arXiv:2603. 00393v2 Announce Type: replace-cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness.
Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution.
The paper introduces a reference‑free instrument that, from a single fit and without an oracle, can detect whether a hybrid PDE‑parameter estimator’s assumed operator is misspecified and distinguish this from mere parameter unidentifiability. In a self‑adjoint parabolic inverse problem, the proposed information‑matrix statistic correctly identifies misspecification with low false‑positive rates, while remaining silent when the design is correctly specified but non‑identifiable. The study demonstrates that conventional accuracy checks can miss significant operator errors, and it maps out the instrument’s blind spots and conditions under which its guarantees hold.
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.