Learning Hybrid Dynamics Models With Simulator-Informed Latent States

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

Exact Inference for Continuous-Time Gaussian Process Dynamics

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors, most methods in Gaussian process (GP) dynamics model learning are trained on one-step ahead predictions. This can become problematic in several scenarios, e.g. if measurements are provided at irregularly-sampled time steps or physical system properties have to be conserved. Thus, we aim for a GP model of the true continuous-time dynamics. Higher-order numerical integrators provide the necessary tools to address this problem by discretizing the dynamics function with arbitrary accuracy. Many higher-order integrators require dynamics evaluations at intermediate time steps making exact GP inference intractable. In previous work, this problem is often tackled by approximating the GP posterior with variational inference. However, exact GP inference is preferable in many scenarios, e.g. due to its mathematical guarantees. In order to make direct inference tractable, we propose to leverage multistep and Taylor integrators. We demonstrate how to derive flexible inference schemes for these types of integrators. Further, we derive tailored sampling schemes that allow to draw consistent dynamics functions from the learned posterior. This is crucial to sample consistent predictions from the dynamics model. We demonstrate empirically and theoretically that our approach yields an accurate representation of the continuous-time system

Combining Slow and Fast: Complementary Filtering for Dynamics Learning

Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions, accumulating errors yield deteriorated long-term behavior. In contrast, models with reliable long-term predictions can often be obtained, either by training a robust but less detailed model, or by leveraging physics-based simulations. In both cases, inaccuracies in the models yield a lack of short-time details. Thus, different models with contrastive properties on different time horizons are available. This observation immediately raises the question: Can we obtain predictions that combine the best of both worlds? Inspired by sensor fusion tasks, we interpret the problem in the frequency domain and leverage classical methods from signal processing, in particular complementary filters. This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other. Essentially, the high-pass filter extracts high-frequencies, whereas the low-pass filter extracts low frequencies. Applying this concept to dynamics model learning enables the construction of models that yield accurate long- and short-term predictions. Here, we propose two methods, one being purely learning-based and the other one being a hybrid model that requires an additional physics-based simulator

Adrenomedullary function, obesity and permissive influences of catecholamines on body mass in patients with chromaffin cell tumours

BACKGROUND Obesity-associated activation of sympathetic nervous outflow is well documented, whereas involvement of dysregulated adrenomedullary hormonal function in obesity is less clear. This study assessed relationships of sympathoadrenal function with indices of obesity and influences of circulating catecholamines on body mass. METHODS Anthropometric and clinical data along with plasma and 24-h urine samples were collected from 590 volunteers and 1368 patients tested for phaeochromocytoma and paraganglioma (PPGL), among whom tumours were diagnosed in 210 individuals. RESULTS Among patients tested for PPGL, those with tumours less often had a body mass index (BMI) above 30 kg/m (12 vs. 31%) and more often a BMI under 25 kg/m (56 vs. 32%) than those without tumours (P < 0.0001). Urinary outputs of catecholamines in patients with PPGL were negatively related to BMI (r = -0.175, P = 0.0133). Post-operative weight gain (P < 0.0001) after resection of PPGL was positively related to presurgical tumoural catecholamine output (r = 0.257, P = 0.0101). Higher BMI in men and women and percent body fat in women of the volunteer group were associated with lower plasma concentrations and urinary outputs of adrenaline and metanephrine, the former indicating obesity-related reduced adrenaline secretion and the latter obesity-related reduced adrenomedullary adrenaline stores. Daytime activity was associated with substantial increases in urinary adrenaline and noradrenaline excretion, with blunted responses in obese subjects. CONCLUSIONS The findings in patients with PPGL support an influence of high circulating catecholamines on body weight. Additional associations of adrenomedullary dysfunction with obesity raise the possibility of a permissive influence of the adrenal medulla on the regulation of body weight