Aug 2026· Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2· 0 citations· 38 references
Computer Science
TL;DR
The Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation, and consistently outperforms competitive baselines in both given-control and missing-control settings, particularly for multi-step and long-horizon forecasting.
Abstract
Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging. Existing approaches that explicitly model system dynamics typically rely on linear assumptions or Koopman-based linearizations, which may inadequately capture complex nonlinear behaviors and lead to error accumulation in long-horizon prediction. To address this limitation, we propose the Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation. Specifically, NBDM leverages Koopman theory to lift the original nonlinear dynamics into a higher-dimensional latent space, where a bilinear dynamical model is constructed to characterize state evolution. To mitigate the approximation error introduced by bilinear representations, we further incorporate a parameterized error compensation term. Within this formulation, control inputs are explicitly integrated into the dynamics, using auxiliary variables when available and learned feedback signals otherwise. To handle scenarios with missing control inputs, we design a memory-enhanced controller that infers latent controls through multiplicative interactions between historical states and control signals. Experiments on five real-world datasets demonstrate that NBDM consistently outperforms competitive baselines in both given-control and missing-control settings, particularly for multi-step and long-horizon forecasting.
Multi-step training of sparse, interpretable models of dynamical systems directly from time-series data yields models with accurate short-term dynamics and strong agreement in long-time statistical properties, including mean, variance, and Lyapunov exponents.
A RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations is proposed and robust satisfaction of the original nonlinear constraints is proved by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state.
The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of dynamical systems, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate models from recordings of dynamics that are inherently nonlinear, such as the response to large perturbations and the evolution on chaotic attractors. Recent approaches attempt to simultaneously fit the linear and nonlinear contributions to the dynamics by performing a regression onto a physically motivated model structure. However, although the resulting nonlinear models can produce accurate short-term predictions, their linearization does not necessarily agree with that of the original system. In this work, we introduce a novel data-driven method --- nonlinearity-subtracted DMD (NSDMD) --- that focuses on producing an accurate linearization of a system when the nonlinear contribution to its dynamics are available while the linear part is not. This scenario is encountered, for example, when the nonlinear terms in the governing equations are known, while the linear operator contains uncertain material properties or it accounts for the closure of unresolved dynamics. This also arises when the data is generated by a black-box simulation code that is able to output the nonlinearity, but not the action of the linear operator on the snapshots. NSDMD leverages data snapshots of the nonlinearity to explicitly account for the purely nonlinear contributions to the dynamics and formulate a regression problem that finds a low-rank approximation of the underlying linear operator. We demonstrate the approach on several numerical examples, showcasing its improved capabilities for data-driven linear analysis of chaotic, partially observed, advection-dominated, and high-dimensional dynamics.
Benjamín Herrmann, Katherine Cao, S. Brunton et al.· 0 citations
This work first learns an implicit spectral predictor using Observation Spectral Filtering using Observation Spectral Filtering, a convex method that competes with the best linear observer for the system, and applies spectral-to-LDS distillation to convert this predictor into an explicit recurrent linear dynamical system.
Liane Galanti, Devan Shah, Shlomo Fortgang et al.· 0 citations
Real-time control of multivariable nonlinear processes requires models balancing high fidelity with computational tractability. This paper compares two data-driven paradigms: Bilinear Koopman Realizations and Physics-Informed Neural Networks. While standard Koopman approaches seek global linearization, we leverage a bilinear framework in the lifted functional space to preserve the natural coupling of control-affine systems. Simultaneously, PINNs ensure physical consistency by embedding conservation laws into the learning objective. To facilitate high-performance control, both surrogate models are integrated into a nonlinear model predictive control scheme using the CasADi framework, enabling efficient algorithmic differentiation for optimization. Simulation results for a quadruple tank system demonstrate that both paradigms reach mean VAF values above 99%, but the Bilinear Koopman model delivers a lower mean RMSE during step transients while doubling the computational speed of the PINN with a Real-Time Factor above 22. We conclude that despite structural scaling limitations regarding neural exploding gradients and operator instability risks, the Bilinear Koopman realization provides a more reliable, noise-resilient solution for real-time hydraulic benchmarks.
Amir Vanegas, Julio Barón-Velandia, Nelson Leonardo Díaz-Aldana et al.· International Conference on...· 0 citations
A stochastic behavioral modeling framework, termed Gaussian behaviors, which augments a deterministic linear time-invariant behavior with a Gaussian noise component is proposed, which enables simple and tractable stochastic data-driven control methods.
András Sasfi, A. Padoan, I. Markovsky et al.· arXiv.org· 0 citations
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