Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation

In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability measure to recover the backward stochastic differential equation (

Holy Grail Math 9 Rigor 7 ·  November 5, 2025

Noise estimation of SDE from a single data trajectory

In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transf

Lab Rats Math 9 Rigor 6 ·  September 29, 2025

Deep Neural Operator Learning for Probabilistic Models

We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for

Holy Grail Math 8.5 Rigor 6 ·  November 10, 2025

Branched Signature Model

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [“Gubinelli, Journal of Differential Equations, 248(4), 2010”], which generalizes the classical geometric rough path. We establish a universal approximation theorem for the branched signature

Lab Rats Math 9 Rigor 2 ·  October 23, 2025

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