FLARE is a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses, and predicts long-horizon high-dimensional responses under inputs not used for training.
Abstract
Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we introduce FLARE, a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses. By estimating latent dimension from data and separating state estimation from external forcing, FLARE enables forecasts to be initialized from past responses and driven by prescribed future inputs. Across known dynamical systems, application-scale forced responses and visual observations, FLARE recovers compact forced dynamics and predicts long-horizon high-dimensional responses under inputs not used for training. By turning learned coordinates into a dynamical interface, FLARE extends equation discovery to systems whose effective states are hidden within complex observations, providing a route for interpretable modelling and prediction of high-dimensional responses in forced dynamical systems.
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.
Mengzhou Gao, Huangqian Yu, Pengfei Jiao· Proceedings of the 32nd ACM...· 0 citations
A factorized latent-conditioning formulation is introduced that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection that enables generalization to previously unseen system instances.
Zi-Tuo Chen, Qiaofeng Li, Jia-Xin Hu et al.· arXiv.org· 1 citation
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.
Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time- stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated 2D wake configurations, a simplified truck wake and the fluidic pinball, we compare Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on Long Short-Term Memory networks. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short- term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.
A. Solera-Rico, Patricia Garc'ia-Caspuenas, C. S. Vila et al.· arXiv.org· 1 citation
Stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability, and output-head replacement shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure.
Neural encoding, decoding, and representation-learning approaches have substantially advanced our ability to predict sensory, behavioral, and cognitive variables from neural population activity. At the same time, dynamical systems approaches increasingly model neural computation as the evolution of latent population states governed by recurrent interactions and structured state transitions. Although these frameworks are often presented as competing paradigms, both can successfully reproduce neural observations while still failing to uniquely identify the computational mechanisms implemented by biological circuits. This perspective argues that this reflects a central unresolved challenge in systems neuroscience: observational recordings alone often provide insufficient constraints for distinguishing mechanistically valid neural dynamics from observationally equivalent alternatives. Accordingly, this perspective proposes a unifying framework integrating representational models, latent neural dynamics, identifiability analysis, and perturbation-based validation within a common mechanistic perspective. First, neural representations are discussed as potentially emerging from temporally localized projections of underlying latent dynamical processes evolving on low-dimensional manifolds. Second, recent advances in learning neural evolution operators using recurrent neural networks, latent state-space models, and dynamical system reconstruction methods are reviewed. Third, it is argued that latent trajectories and predictive performance alone do not guarantee mechanistic validity because multiple latent organizations and evolution operators may remain observationally equivalent despite implying distinct causal mechanisms. Finally, perturbation, intervention, and closed-loop neural interfaces are discussed as additional causal constraints capable of falsifying candidate dynamical explanations under targeted manipulation. Across these four principles, the central challenge in modern neuroscience is framed not simply as decoding neural activity or reconstructing latent trajectories, but as determining which inferred dynamical operators remain predictive under intervention and how perturbation can reduce the admissible class of observationally equivalent candidate mechanisms. From this perspective, evolution operators become experimentally testable hypotheses rather than purely descriptive latent models. Integrating latent dynamical modeling with perturbation-based validation may therefore support a transition from prediction-oriented neuroscience toward perturbation-constrained mechanistic dynamical neuroscience.
Armin Hakkak Moghadam Torbati· Journal of Neural Engineerin...· 0 citations
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