Papers for

computational physicists

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Deep operator learning speeds up sampling for complex stochastic systems

Deep operator learning for efficient sampling from invariant measures of stochastic differential equations

Abstract: We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.

Thu 10 SeptMachine Learning
The gist
Sampling from complex random systems described by stochastic differential equations (SDEs) is often slow and computationally expensive. The authors created a neural network-based sampler that learns how to generate samples from a wide range of these systems after initial training. This method then produces samples quickly for new problems without the usual long wait times. They also showed that their approach works well even for very high-dimensional problems where traditional methods fail.
Open → 2609.11376v1

Learning recovers optimal diagonal regularizers for noisy inverse problems

Why Learning Rediscovers the Closed-Form Diagonal Regularizer

Abstract: We identify a diagonal saturation principle in modal inverse problems: when truncation noise is isotropic, the Bayes-optimal Tikhonov shape is a closed-form power law Gamma_k proportional to lambda_k^|s| set by the prior alone, independent of the domain. Berry's random-wave conjecture decorrelates the truncation noise across modes, and Weyl's eigenvalue counting law supplies enough modes for the conclusion to survive empirical Berry violations. Together they predict an approximately flat loss landscape across the per-mode family, leaving narrow scope for a diagonal regularizer to robustly beat the closed form. On FEM-simulated acoustic rooms, the closed form is near-optimal relative to per-room oracle tuning across observation windows, and three diagonal architectures trained on the same data match its reconstruction error within 1 pp despite learning qualitatively different spectra. The framework extends to heat diffusion via a known exponential Green's function correction with no new free parameters. Saturation is restricted to the diagonal family: Learned Iterative Ridge crosses the boundary by exploiting cross-mode coupling, locating where learning starts to help.

Wed 9 SeptMachine LearningRobotics
The gist
When solving problems where data is noisy and incomplete, a common technique adjusts solutions using simple diagonal weighting. The authors found that the best way to do this weighting follows a specific pattern set only by prior knowledge, not details of the problem. This pattern explains why different learned diagonal adjustments perform almost the same. However, methods that consider interactions between different parts start to improve beyond this limit. Testing was done on simulated sound problems and heat diffusion models.
Open → 2609.09656v1