Learning Adaptive Wiener Processes for Stochastic Financial Datasets with Physics-Informed Kolmogorov-Arnold Encoder-Decoder Networks

Joy Dip Das, Ruppa Thulasiram
Proceedings of the The 39th Canadian Conference on Artificial Intelligence, PMLR 318:903-908, 2026.

Abstract

Financial time series are non-stationary, heavy-tailed, and regime dependent, which complicates price forecasting and undermines the robustness of standard machine learning and deep learning models across assets. This work proposes a physics-informed framework, Adaptive Wiener KAN-RNN, that learns stochastic dynamics of the underlying financial dataset by operating directly in stochastic differential equation (SDE) parameter space: a Kolmogorov–Arnold Network (KAN) encoder transforms 120-day price windows into spline-based functional features tailored to drift ($\mu$_t) and log-volatility (log $\sigma$_t), and a long short-term memory (LSTM) or gated recurrent unit (GRU) decoder models their temporal evolution as latent state processes. A Wiener-process-based loss enforces consistency with geometric Brownian motion (GBM) by aligning the distribution of simulated and realized price paths, ensuring that the learned parameters remain stochastically coherent. Experiments on technology equities, including Apple (AAPL) and Microsoft (MSFT), show that this architecture delivers systematically lower error metrics and near-perfect explanatory power compared with dense KAN and conventional LSTM/GRU baselines, while yielding interpretable time-varying estimates of market drift and volatility.

Cite this Paper

BibTeX
@InProceedings{pmlr-v318-das26a, title = {Learning Adaptive Wiener Processes for Stochastic Financial Datasets with Physics-Informed Kolmogorov-Arnold Encoder-Decoder Networks}, author = {Das, Joy Dip and Thulasiram, Ruppa}, booktitle = {Proceedings of the The 39th Canadian Conference on Artificial Intelligence}, pages = {903--908}, year = {2026}, editor = {Bouzar-Benlabiod, Lydia and Leung, Carson}, volume = {318}, series = {Proceedings of Machine Learning Research}, month = {25--29 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v318/main/assets/das26a/das26a.pdf}, url = {https://proceedings.mlr.press/v318/das26a.html}, abstract = {Financial time series are non-stationary, heavy-tailed, and regime dependent, which complicates price forecasting and undermines the robustness of standard machine learning and deep learning models across assets. This work proposes a physics-informed framework, Adaptive Wiener KAN-RNN, that learns stochastic dynamics of the underlying financial dataset by operating directly in stochastic differential equation (SDE) parameter space: a Kolmogorov–Arnold Network (KAN) encoder transforms 120-day price windows into spline-based functional features tailored to drift ($\mu$_t) and log-volatility (log $\sigma$_t), and a long short-term memory (LSTM) or gated recurrent unit (GRU) decoder models their temporal evolution as latent state processes. A Wiener-process-based loss enforces consistency with geometric Brownian motion (GBM) by aligning the distribution of simulated and realized price paths, ensuring that the learned parameters remain stochastically coherent. Experiments on technology equities, including Apple (AAPL) and Microsoft (MSFT), show that this architecture delivers systematically lower error metrics and near-perfect explanatory power compared with dense KAN and conventional LSTM/GRU baselines, while yielding interpretable time-varying estimates of market drift and volatility.} }
Endnote
%0 Conference Paper %T Learning Adaptive Wiener Processes for Stochastic Financial Datasets with Physics-Informed Kolmogorov-Arnold Encoder-Decoder Networks %A Joy Dip Das %A Ruppa Thulasiram %B Proceedings of the The 39th Canadian Conference on Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Lydia Bouzar-Benlabiod %E Carson Leung %F pmlr-v318-das26a %I PMLR %P 903--908 %U https://proceedings.mlr.press/v318/das26a.html %V 318 %X Financial time series are non-stationary, heavy-tailed, and regime dependent, which complicates price forecasting and undermines the robustness of standard machine learning and deep learning models across assets. This work proposes a physics-informed framework, Adaptive Wiener KAN-RNN, that learns stochastic dynamics of the underlying financial dataset by operating directly in stochastic differential equation (SDE) parameter space: a Kolmogorov–Arnold Network (KAN) encoder transforms 120-day price windows into spline-based functional features tailored to drift ($\mu$_t) and log-volatility (log $\sigma$_t), and a long short-term memory (LSTM) or gated recurrent unit (GRU) decoder models their temporal evolution as latent state processes. A Wiener-process-based loss enforces consistency with geometric Brownian motion (GBM) by aligning the distribution of simulated and realized price paths, ensuring that the learned parameters remain stochastically coherent. Experiments on technology equities, including Apple (AAPL) and Microsoft (MSFT), show that this architecture delivers systematically lower error metrics and near-perfect explanatory power compared with dense KAN and conventional LSTM/GRU baselines, while yielding interpretable time-varying estimates of market drift and volatility.
APA
Das, J.D. & Thulasiram, R.. (2026). Learning Adaptive Wiener Processes for Stochastic Financial Datasets with Physics-Informed Kolmogorov-Arnold Encoder-Decoder Networks. Proceedings of the The 39th Canadian Conference on Artificial Intelligence, in Proceedings of Machine Learning Research 318:903-908 Available from https://proceedings.mlr.press/v318/das26a.html.

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