Learning Hybrid Dynamics Models With Simulator-Informed Latent States

TL;DR

This work tackles the challenge of learning dynamic systems from partial measurements when a physics-based simulator is available only as a black box. It introduces a hybrid KKL–RNN model that partitions latent states into observables driven by the simulator (OVS) and independently learned non-OVS states, with a trainable KKL observer continually correcting the OVS states using simulator outputs. By coupling an observer-based latent state correction to a residual RNN, the approach achieves accurate short- and long-term predictions, buffers missing simulator information, and yields a robust, physically meaningful dynamic representation. The method outperforms baselines including purely learning-based and other hybrid architectures, especially when the simulator is partially informative, and can be extended to pure learning scenarios with a simulator substitute.

Abstract

Dynamics model learning deals with the task of inferring unknown dynamics from measurement data and predicting the future behavior of the system. A typical approach to address this problem is to train recurrent models. However, predictions with these models are often not physically meaningful. Further, they suffer from deteriorated behavior over time due to accumulating errors. Often, simulators building on first principles are available being physically meaningful by design. However, modeling simplifications typically cause inaccuracies in these models. Consequently, hybrid modeling is an emerging trend that aims to combine the best of both worlds. In this paper, we propose a new approach to hybrid modeling, where we inform the latent states of a learned model via a black-box simulator. This allows to control the predictions via the simulator preventing them from accumulating errors. This is especially challenging since, in contrast to previous approaches, access to the simulator's latent states is not available. We tackle the task by leveraging observers, a well-known concept from control theory, inferring unknown latent states from observations and dynamics over time. In our learning-based setting, we jointly learn the dynamics and an observer that infers the latent states via the simulator. Thus, the simulator constantly corrects the latent states, compensating for modeling mismatch caused by learning. To maintain flexibility, we train an RNN-based residuum for the latent states that cannot be informed by the simulator.

Figures (3)

• Figure 1: High-level overview of our method. Transition model (left): The simulator signal $\hat{s}$ is fed into a trainable observer to infer the OVS states $u$. The non-OVS states $v$ are learned by an additional RNN. Observation model (right): The simulator is reconstructed by $h_{\theta}$, while $g_{\theta}$ and $r_{\theta}$ reconstruct the measurements.
• Figure 2: Rollouts over time for system i) with our hybrid KKL-RNN (left) and with the hybrid GRU (right). The training horizon is marked with dotted lines. The results demonstrate that our method reproduces all components correctly and learns a plausible split in OVS and non-OVS. The hybrid GRU shows deteriorated and unphysical long-term behavior.
• Figure 3: The rollouts with our KKL-RNN for System iii) (left) show that our method learns a plausible split into OVS and non-OVS and is able to buffer missing simulator inputs. The rollouts for System ii) (middle) demonstrate that our KKL-RNN produces more accurate results than the other HM approaches. The residual model even shows unphysical behavior. Accumulating errors in the baseline are further visible in the RMSE over time for System (ii) (right).