Loss formulations for assumption-free neural inference of SDE coefficient functions

• Published in: NPJ systems biology and applications Vol. 11; no. 1; pp. 22 - 10
• Main Authors: Vaisband, Marc, von Bornhaupt, Valentin, Schmid, Nina, Abulizi, Izdar, Hasenauer, Jan
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.03.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 631/553/2393; 631/553/2695; 631/553/2700; 631/553/2709; Algorithms; Bioinformatics; Biology; Biomedical and Life Sciences; Brownian motion; Computational Biology/Bioinformatics; Computer Appl. in Life Sciences; Computer Simulation; Deep learning; Dynamical systems; Life Sciences; Medical research; Neural networks; Neural Networks, Computer; Ordinary differential equations; Simulation; Stochastic Processes; Systems Biology
• ISSN: 2056-7189; 2056-7189
• DOI: 10.1038/s41540-025-00500-6

Stochastic differential equations (SDEs) are one of the most commonly studied probabilistic dynamical systems, and widely used to model complex biological processes. Building upon the previously introduced idea of performing inference of dynamical systems by parametrising their coefficient functions via neural networks, we propose a novel formulation for an optimisation objective that combines simulation-based penalties with pseudo-likelihoods. This greatly improves prediction performance compared to the state-of-the-art, and makes it possible to learn a wide variety of dynamics without any prior assumptions on analytical structure.