arXiv subjects

Gajanan V. Honnavar

Publications and source records attributed to Gajanan V. Honnavar.

3 recordsLinked to original sources

arXiv2026

PhysSAE: Mechanistic Interpretability of PINNs with Sparse Autoencoders

Physics-Informed Neural Networks (PINNs) embed PDE residuals into neural network training, but their internal representations remain opaque: it is unknown what physical features their hidden layers encode or whether those features have a localized causal role. We present PhysSAE, a mechanistic interpretability framework that trains overcomplete sparse autoencoders (SAEs) on PINN penultimate-layer activations and evaluates dictionary atoms through direct causal intervention in the original frozen hidden state: $h_{\mathrm{cf}} = h - αz_k d_k$, bypassing the SAE decoder entirely. Across six PDE families, with 3 PINN seeds and 3 SAE seeds each---we show that (i) Our discovered SAE atoms align with independently-defined physical observables (max Pearson $|r|=0.951$, always $\gg$ permutation null), (ii) the causal footprint of top-aligned atom ablation is 1.2--4.2$\times$ more spatially concentrated canonical than PCA or ICA interventions, and (iii) top-aligned atoms outperform matched random controls on causal localization for structured physical concepts (ESF$_{80}$ advantage 0.04-0.44). Two-atom bilateral representations improve concept regression R$^2$ by $ΔR^2\!=\!0.05\text{-}0.15$ over single atoms, while random pairs decrease it by up to 0.60. These results demonstrate that PINNs develop sparse, physically structured latent representations that can be identified and causally interrogated post-hoc, opening a path toward interpretability-aware scientific machine learning.

cs.LG↗

arXiv2026

Weak Form Recovery of Heston Type Stochastic Dynamics

Estimating the coupled drift, diffusion, and leverage structure of a stochastic-volatility model directly from a price path is an unresolved inverse problem: Kramers--Moyal increment estimators amplify sampling noise as the step shrinks, weak-form SINDy has not been extended to coupled two-dimensional diffusions or to the return--variance cross-variation producing leverage, and Heston calibration typically relies on option-implied surfaces rather than the physical-measure path. We extend the spatial weak-form Galerkin framework to the Heston model: variance increments, squared variance increments, squared price increments, and their cross-product are projected onto shared Gaussian kernels in variance space, giving one LASSO regression that jointly recovers mean reversion $κ$, long-run variance $θ$, vol-of-vol $ξ$, and leverage correlation $ρ$, with a drift-informed bias correction analogous to scalar-SDE diffusion debiasing. Across 30 daily-observed Heston simulations, $ξ$, $ρ$, and $ρξ$ are recovered with median errors under 2\%. Applied to S\&P 500 data spanning the 2007--2010 crisis, the method recovers negative leverage consistent with the documented equity leverage effect, and a 50-stock Indian panel shows the same sign under several independent variance proxies.

physics.data-an↗

arXiv2026

Data-Driven Weak-form Discovery of Stochastic Systems

We present an algorithm for learning the governing equations of a stochastic dynamical system from trajectory data. It recovers interpretable symbolic expressions for both the drift $b(x)$ and the diffusion $a(x)$ in a single pass, yielding a model that can be queried directly for relaxation timescales, metastable escape rates, and stationary distributions. Rather than estimating the dynamics one time step at a time, the algorithm averages each candidate term across the whole trajectory before regressing; a drift-informed correction further removes the finite-sampling bias in the diffusion estimate, cutting it from 4.6% to 0.6% for state-dependent noise. We also show that the trajectory averaging must use a spatial rather than a temporal weighting: temporal weighting, as in existing weak-form methods, is biased for stochastic data with an error that grows with dataset size. On three benchmark systems -- the Ornstein--Uhlenbeck process, a double-well Langevin system, and a multiplicative-noise system -- the algorithm recovers all coefficients to within 5%, stationary densities to within 0.01 in total variation, and escape rates that match the true dynamics.

stat.ME↗