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ARXIV:2605.15407 · BAYESIAN INFERENCE · SUBMITTED 18 MAY · 20:34 UTC · FRESHNESS STALE
ARXIV:2605.15407BAYESIAN INFERENCESUBMITTED 18 MAY · 20:34 UTCFRESHNESS STALEHojjat Kaveh · Ricardo Baptista · Andrew M. Stuart · arXiv
Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems.
Opportunity summary
Pain Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation,…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving…
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The results show that the learned transport captures posterior structure, including multimodality and dominant modes, while enabling fast posterior sampling for new observations.
Bayesian Inference moved forward this cycle; last verified May 2026. Public score 2.0/10.
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Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems.
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10.48550/arXiv.2605.15407Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems.
Abstract
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationally prohibitive when inference must be repeated many times. We propose a transport-based approach that learns an observation-dependent map pushing forward a reference measure to approximate the posterior distribution. The map is trained by minimizing an averaged energy-distance objective between the true posterior and the learned pushforward. This formulation is likelihood-free, requiring only joint samples, and avoids density evaluation, invertibility constraints, and Jacobian determinant computations. For function-space inverse problems with Gaussian priors, we parameterize the transport map as the identity plus a perturbation in the Cameron-Martin space of the prior, preserving absolute continuity with respect to the prior. In infinite-dimensional settings, the map is represented using neural operators. We illustrate the method on a finite-dimensional nonlinear inverse problem and two PDE-constrained inverse problems arising in porous medium flow and seismic inversion. The results show that the learned transport captures posterior structure, including multimodality and dominant modes, while enabling fast posterior sampling for new observations.
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PROBLEM
Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationa...
METHOD
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each ob...
RESULT
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The results show that the learned transport captures posterior structure, including multimodality and dominant modes, while enabling fast posterior sampling for new observations.
WHY NOW
Bayesian Inference moved forward this cycle; last verified May 2026. Public score 2.0/10.
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Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationally prohibitive when inference must be repeated many times.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationally prohibitive when inference must be repeated many times.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 2.0/10 on the public viability pass. The results show that the learned transport captures posterior structure, including multimodality and dominant modes, while enabling fast posterior sampling for new observations.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Bayesian Inference moved forward this cycle; last verified May 2026. Public score 2.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Introduces an amortized, likelihood-free Bayesian inference method using transport maps and neural operators for nonlinear inverse problems.
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