Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the model and measurements, and optimal (in the Bayesian sense) recursive formulations e.g. the Kalman Filter. However, they require significant domain knowledge to derive the parametric form and considerable hand-tuning to correctly set all the parameters. Data driven techniques e.g. Recurrent Neural Networks have emerged as compelling alternatives to SSMs with wide success across a number of challenging tasks, in part due to their ability to extract relevant features from rich inputs. They however lack interpretability and robustness to unseen conditions. In this work, we present DynaNet, a hybrid deep learning and time-varying state-space model which can be trained end-to-end. Our neural Kalman dynamical model allows us to exploit the relative merits of each approach. We demonstrate state-of-the-art estimation and prediction on a number of physically challenging tasks, including visual odometry, sensor fusion for visual-inertial navigation and pendulum control. In addition we show how DynaNet can indicate failures through investigation of properties such as the rate of innovation (Kalman Gain).
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Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in data-driven modeling techniques, in particular neural networks have proven to provide an effective framework for solving a wide range of tasks. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.
While most classic studies of function in experimental neuroscience have focused on the coding properties of individual neurons, recent developments in recording technologies have resulted in an increasing emphasis on the dynamics of neural populations. This has given rise to a wide variety of models for analyzing population activity in relation to experimental variables, but direct testing of many neural population hypotheses requires intervening in the system based on current neural state, necessitating models capable of inferring neural state online. Existing approaches, primarily based on dynamical systems, require strong parametric assumptions that are easily violated in the noise-dominated regime and do not scale well to the thousands of data channels in modern experiments. To address this problem, we propose a method that combines fast, stable dimensionality reduction with a soft tiling of the resulting neural manifold, allowing dynamics to be approximated as a probability flow between tiles. This method can be fit efficiently using online expectation maximization, scales to tens of thousands of tiles, and outperforms existing methods when dynamics are noise-dominated or feature multi-modal transition probabilities. The resulting model can be trained at kiloHertz data rates, produces accurate approximations of neural dynamics within minutes, and generates predictions on submillisecond time scales. It retains predictive performance throughout many time steps into the future and is fast enough to serve as a component of closed-loop causal experiments.
This paper introduces a novel proprioceptive state estimator for legged robots based on a learned displacement measurement from IMU data. Recent research in pedestrian tracking has shown that motion can be inferred from inertial data using convolutional neural networks. A learned inertial displacement measurement can improve state estimation in challenging scenarios where leg odometry is unreliable, such as slipping and compressible terrains. Our work learns to estimate a displacement measurement from IMU data which is then fused with traditional leg odometry. Our approach greatly reduces the drift of proprioceptive state estimation, which is critical for legged robots deployed in vision and lidar denied environments such as foggy sewers or dusty mines. We compared results from an EKF and an incremental fixed-lag factor graph estimator using data from several real robot experiments crossing challenging terrains. Our results show a reduction of relative pose error by 37% in challenging scenarios when compared to a traditional kinematic-inertial estimator without learned measurement. We also demonstrate a 22% reduction in error when used with vision systems in visually degraded environments such as an underground mine.
Deep learning-based models, such as recurrent neural networks (RNNs), have been applied to various sequence learning tasks with great success. Following this, these models are increasingly replacing classic approaches in object tracking applications for motion prediction. On the one hand, these models can capture complex object dynamics with less modeling required, but on the other hand, they depend on a large amount of training data for parameter tuning. Towards this end, we present an approach for generating synthetic trajectory data of unmanned-aerial-vehicles (UAVs) in image space. Since UAVs, or rather quadrotors are dynamical systems, they can not follow arbitrary trajectories. With the prerequisite that UAV trajectories fulfill a smoothness criterion corresponding to a minimal change of higher-order motion, methods for planning aggressive quadrotors flights can be utilized to generate optimal trajectories through a sequence of 3D waypoints. By projecting these maneuver trajectories, which are suitable for controlling quadrotors, to image space, a versatile trajectory data set is realized. To demonstrate the applicability of the synthetic trajectory data, we show that an RNN-based prediction model solely trained on the generated data can outperform classic reference models on a real-world UAV tracking dataset. The evaluation is done on the publicly available ANTI-UAV dataset.
Dynamical systems models for controlling multi-agent swarms have demonstrated advances toward resilient, decentralized navigation algorithms. We previously introduced the NeuroSwarms controller, in which agent-based interactions were modeled by analogy to neuronal network interactions, including attractor dynamics and phase synchrony, that have been theorized to operate within hippocampal place-cell circuits in navigating rodents. This complexity precludes linear analyses of stability, controllability, and performance typically used to study conventional swarm models. Further, tuning dynamical controllers by hand or grid search is often inadequate due to the complexity of objectives, dimensionality of model parameters, and computational costs of simulation-based sampling. Here, we present a framework for tuning dynamical controller models of autonomous multi-agent systems based on Bayesian Optimization (BayesOpt). Our approach utilizes a task-dependent objective function to train Gaussian Processes (GPs) as surrogate models to achieve adaptive and efficient exploration of a dynamical controller model's parameter space. We demonstrate this approach by studying an objective function selecting for NeuroSwarms behaviors that cooperatively localize and capture spatially distributed rewards under time pressure. We generalized task performance across environments by combining scores for simulations in distinct geometries. To validate search performance, we compared high-dimensional clustering for high- vs. low-likelihood parameter points by visualizing sample trajectories in Uniform Manifold Approximation and Projection (UMAP) embeddings. Our findings show that adaptive, sample-efficient evaluation of the self-organizing behavioral capacities of complex systems, including dynamical swarm controllers, can accelerate the translation of neuroscientific theory to applied domains.
An outstanding challenge with safety methods for human-robot interaction is reducing their conservatism while maintaining robustness to variations in human behavior. In this work, we propose that robots use confidence-aware game-theoretic models of human behavior when assessing the safety of a human-robot interaction. By treating the influence between the human and robot as well as the human's rationality as unobserved latent states, we succinctly infer the degree to which a human is following the game-theoretic interaction model. We leverage this model to restrict the set of feasible human controls during safety verification, enabling the robot to confidently modulate the conservatism of its safety monitor online. Evaluations in simulated human-robot scenarios and ablation studies demonstrate that imbuing safety monitors with confidence-aware game-theoretic models enables both safe and efficient human-robot interaction. Moreover, evaluations with real traffic data show that our safety monitor is less conservative than traditional safety methods in real human driving scenarios.
Quantification of economic uncertainty is a key concept for the prediction of macro economic variables such as gross domestic product (GDP), and it becomes particularly relevant on real-time or short-time predictions methodologies, such as nowcasting, where it is required a large amount of time series data, commonly with different structures and frequencies. Most of the data comes from the official agencies statistics and non-public institutions, however, relying our estimates in just the traditional data mentioned before, have some disadvantages. One of them is that economic uncertainty could not be represented or measured in a proper way based solely in financial or macroeconomic data, another one, is that they are susceptible to lack of information due to extraordinary events, such as the current COVID-19 pandemic. For these reasons, it is very common nowadays to use some non-traditional data from different sources, such as social networks or digital newspapers, in addition to the traditional data from official sources. The economic policy uncertainty (EPU) index, is the most used newspaper-based indicator to quantify the uncertainty, and is based on topic modeling of newspapers. In this paper, we propose a methodology to estimate the EPU index, which incorporates a fast and efficient method for topic modeling of digital news based on semantic clustering with word embeddings, allowing to update the index in real-time, which is a drawback with another proposals that use computationally intensive methods for topic modeling, such as Latent Dirichlet Allocation (LDA). We show that our proposal allow us to update the index and significantly reduces the time required for new document assignation into topics.
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed robust testing approaches are applicable both in the case of discrete and continuous time models. Both of the methods use the Cauchy estimator to effectively handle the problems of endogeneity, persistence and/or fat-tailedness in regressors and errors. The difference between our two methods is how the heterogeneous volatility is controlled. The first method relies on robust t-statistic inference using group estimators of a regression parameter of interest proposed in Ibragimov and Muller, 2010. It is simple to implement, but requires the exogenous volatility assumption. To relax the exogenous volatility assumption, we propose another method which relies on the nonparametric correction of volatility. The proposed methods perform well compared with widely used alternative inference procedures in terms of their finite sample properties.
Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.
We present R-LINS, a lightweight robocentric lidar-inertial state estimator, which estimates robot ego-motion using a 6-axis IMU and a 3D lidar in a tightly-coupled scheme. To achieve robustness and computational efficiency even in challenging environments, an iterated error-state Kalman filter (ESKF) is designed, which recursively corrects the state via repeatedly generating new corresponding feature pairs. Moreover, a novel robocentric formulation is adopted in which we reformulate the state estimator concerning a moving local frame, rather than a fixed global frame as in the standard world-centric lidar-inertial odometry(LIO), in order to prevent filter divergence and lower computational cost. To validate generalizability and long-time practicability, extensive experiments are performed in indoor and outdoor scenarios. The results indicate that R-LINS outperforms lidar-only and loosely-coupled algorithms, and achieve competitive performance as the state-of-the-art LIO with close to an order-of-magnitude improvement in terms of speed.
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