Researchers Xianglin Wu, Chiheb Ben Hammouda, and Cornelis W. Oosterlee from the Delft University of Technology have developed a novel approach to improve the accuracy and efficiency of parameter estimation in complex stochastic systems. Their work, published in the Journal of Computational Physics, focuses on integrating path signatures with deep learning architectures to model systems with rough dynamics and long-range dependence, such as those encountered in quantitative finance and reliability engineering.
Stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) are often used to model these systems. However, their non-Markovian nature and lack of semimartingale structure make traditional parameter estimation techniques difficult to apply. The researchers investigated whether integrating path signatures into deep learning architectures could improve the trade-off between estimation accuracy and model complexity. They also explored what constitutes an effective architecture for leveraging signatures as feature maps.
The team introduced SigMA, a neural architecture that combines path signatures with multi-head self-attention, supported by a convolutional preprocessing layer and a multilayer perceptron for effective feature encoding. SigMA learns model parameters from synthetically generated paths of fBm-driven SDEs, including fractional Brownian motion, fractional Ornstein-Uhlenbeck, and rough Heston models. It focuses particularly on estimating the Hurst parameter and joint multi-parameter inference, and it generalizes robustly to unseen trajectories.
Extensive experiments on synthetic data and two real-world datasets—equity-index realized volatility and Li-ion battery degradation—showed that SigMA consistently outperforms CNN, LSTM, vanilla Transformer, and Deep Signature baselines in accuracy, robustness, and model compactness. These results demonstrate that combining signature transforms with attention-based architectures provides an effective and scalable framework for parameter inference in stochastic systems with rough or persistent temporal structure.
For the energy sector, this research could have practical applications in improving the modeling and prediction of complex systems, such as battery degradation in energy storage systems or the volatility of energy markets. By providing more accurate and efficient parameter estimation, SigMA could enhance decision-making processes and optimize resource allocation in energy systems.
This article is based on research available at arXiv.