Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression

Developing mathematical models of dynamic systems is central to many disciplines of engineering and science. Models facilitate simulations, analysis of the system's behavior, decision making and design of automatic control algorithms. Even inherently model-free control techniques such as reinforcement learning (RL) have been shown to benefit from the use of models, typically learned online. Any model construction method must address the tradeoff between the accuracy of the model and its complexity, which is difficult to strike. In this paper, we propose to employ symbolic regression (SR) to construct parsimonious process models described by analytic equations. We have equipped our method with two different state-of-the-art SR algorithms which automatically search for equations that fit the measured data: Single Node Genetic Programming (SNGP) and Multi-Gene Genetic Programming (MGGP). In addition to the standard problem formulation in the state-space domain, we show how the method can also be applied to input-output models of the NARX (nonlinear autoregressive with exogenous input) type. We present the approach on three simulated examples with up to 14-dimensional state space: an inverted pendulum, a mobile robot, and a bipedal walking robot. A comparison with deep neural networks and local linear regression shows that SR in most cases outperforms these commonly used alternative methods. We demonstrate on a real pendulum system that the analytic model found enables a RL controller to successfully perform the swing-up task, based on a model constructed from only 100 data samples

Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data. Historically, symbolic regression has been predominantly realized by genetic programming, a method that evolves populations of candidate solutions that are subsequently modified by genetic operators crossover and mutation. However, this approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data - models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic model, i.e., its structure and the coefficients, using gradient-based optimization algorithms. This paper proposes a novel neural network-based symbolic regression method that constructs physically plausible models based on even very small training data sets and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all the models generated throughout the whole learning process. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system. The results clearly show the potential of the method to find parsimonious models that comply with the prior knowledge provided

Invasive annual grasses—Reenvisioning approaches in a changing climate

For nearly a century, invasive annual grasses have increasingly impacted terrestrial ecosystems across the western United States. Weather variability associated with climate change and increased atmospheric carbon dioxide (CO2) are making even more difficult the challenges of managing invasive annual grasses. As part of a special issue on climate change impacts on soil and water conservation, the topic of invasive annual grasses is being addressed by scientists at the USDA Agricultural Research Service to emphasize the need for additional research and future studies that build on current knowledge and account for (extreme) changes in abiotic and biotic conditions. Much research has focused on understanding the mechanisms underlying annual grass invasion, as well as assessing patterns and responses from a wide range of disturbances and management approaches. Weather extremes and the increasing occurrences of wildfire are contributing to the complexity of the problem. In broad terms, invasive annual grass management, including restoration, must be proactive to consider human values and ecosystem resiliency. Models capable of synthesizing vast amounts of diverse information are necessary for creating trajectories that could result in the establishment of perennial systems. Organization and collaboration are needed across the research community and with land managers to strategically develop and implement practices that limit invasive annual grasses. In the future, research will need to address invasive annual grasses in an adaptive integrated weed management (AIWM) framework that utilizes models and accounts for climate change that is resulting in altered/new approaches to management and restoration

Car Detection on a Mobile Robot by Fusing Visual and 3D Lidar Data

katedra řídicí technik

Beyond the Safeguards: Exploring the Security Risks of ChatGPT

The increasing popularity of large language models (LLMs) such as ChatGPT has led to growing concerns about their safety, security risks, and ethical implications. This paper aims to provide an overview of the different types of security risks associated with ChatGPT, including malicious text and code generation, private data disclosure, fraudulent services, information gathering, and producing unethical content. We present an empirical study examining the effectiveness of ChatGPT's content filters and explore potential ways to bypass these safeguards, demonstrating the ethical implications and security risks that persist in LLMs even when protections are in place. Based on a qualitative analysis of the security implications, we discuss potential strategies to mitigate these risks and inform researchers, policymakers, and industry professionals about the complex security challenges posed by LLMs like ChatGPT. This study contributes to the ongoing discussion on the ethical and security implications of LLMs, underscoring the need for continued research in this area

Symbolic regression driven by training data and prior knowledge

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error does not provide sufficient guidance toward desired models. Standard symbolic regression techniques then yield models that are partially incorrect, for instance, in terms of their steady-state characteristics or local behavior. If these properties were considered already during the search process, more accurate and relevant models could be produced. We propose a multi-objective symbolic regression approach that is driven by both the training data and the prior knowledge of the properties the desired model should manifest. The properties given in the form of formal constraints are internally represented by a set of discrete data samples on which candidate models are exactly checked. The proposed approach was experimentally evaluated on three test problems with results clearly demonstrating its capability to evolve realistic models that fit the training data well while complying with the prior knowledge of the desired model characteristics at the same time. It outperforms standard symbolic regression by several orders of magnitude in terms of the mean squared deviation from a reference model.</p

Selecting Informative Data Samples for Model Learning Through Symbolic Regression

Continual model learning for nonlinear dynamic systems, such as autonomous robots, presents several challenges. First, it tends to be computationally expensive as the amount of data collected by the robot quickly grows in time. Second, the model accuracy is impaired when data from repetitive motions prevail in the training set and outweigh scarcer samples that also capture interesting properties of the system. It is not known in advance which samples will be useful for model learning. Therefore, effective methods need to be employed to select informative training samples from the continuous data stream collected by the robot. Existing literature does not give any guidelines as to which of the available sample-selection methods are suitable for such a task. In this paper, we compare five sample-selection methods, including a novel method using the model prediction error. We integrate these methods into a model learning framework based on symbolic regression, which allows for learning accurate models in the form of analytic equations. Unlike the currently popular data-hungry deep learning methods, symbolic regression is able to build models even from very small training data sets. We demonstrate the approach on two real robots: the TurtleBot mobile robot and the Parrot Bebop drone. The results show that an accurate model can be constructed even from training sets as small as 24 samples. Informed sample-selection techniques based on prediction error and model variance clearly outperform uninformed methods, such as sequential or random selection.Learning & Autonomous Contro

Visual Navigation in Real-World Indoor Environments Using End-to-End Deep Reinforcement Learning

Visual navigation is essential for many applications in robotics, from manipulation, through mobile robotics to automated driving. Deep reinforcement learning (DRL) provides an elegant map-free approach integrating image processing, localization, and planning in one module, which can be trained and therefore optimized for a given environment. However, to date, DRL-based visual navigation was validated exclusively in simulation, where the simulator provides information that is not available in the real world, e.g., the robot's position or segmentation masks. This precludes the use of the learned policy on a real robot. Therefore, we present a novel approach that enables a direct deployment of the trained policy on real robots. We have designed a new powerful simulator capable of domain randomization. To facilitate the training, we propose visual auxiliary tasks and a tailored reward scheme. The policy is fine-tuned on images collected from real-world environments. We have evaluated the method on a mobile robot in a real office environment. The training took approximately 30 hours on a single GPU. In 30 navigation experiments, the robot reached a 0.3-meter neighbourhood of the goal in more than 86.7% of cases. This result makes the proposed method directly applicable to tasks like mobile manipulation.Learning & Autonomous Contro

Multi-objective symbolic regression for physics-aware dynamic modeling

Virtually all dynamic system control methods benefit from the availability of an accurate mathematical model of the system. This includes also methods like reinforcement learning, which can be vastly sped up and made safer by using a dynamic system model. However, obtaining a sufficient amount of informative data for constructing dynamic models can be difficult. Consequently, standard data-driven model learning techniques using small data sets that do not cover all important properties of the system yield models that are partly incorrect, for instance, in terms of their steady-state characteristics or local behavior. However, often some knowledge about the desired physical properties of the model is available. Recently, several symbolic regression approaches making use of such knowledge to compensate for data insufficiency were proposed. Therefore, this knowledge should be incorporated into the model learning process to compensate for data insufficiency. In this paper, we consider a multi-objective symbolic regression method that optimizes models with respect to their training error and the measure of how well they comply with the desired physical properties. We propose an extension to the existing algorithm that helps generate a diverse set of high-quality models. Further, we propose a method for selecting a single final model out of the pool of candidate output models. We experimentally demonstrate the approach on three real systems: the TurtleBot 2 mobile robot, the Parrot Bebop 2 drone and the magnetic manipulation system. The results show that the proposed model-learning algorithm yields accurate models that are physically justified. The improvement in terms of the model's compliance with prior knowledge over the models obtained when no prior knowledge was involved in the learning process is of several orders of magnitude.Accepted Author ManuscriptLearning & Autonomous Contro

Symbolic Regression Methods for Reinforcement Learning

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as neural networks or basis function expansions, have two main drawbacks: They are black-box models offering little insight into the mappings learned, and they require extensive trial and error tuning of their hyper-parameters. In this paper, we propose a new approach to constructing smooth value functions in the form of analytic expressions by using symbolic regression. We introduce three off-line methods for finding value functions based on a state-transition model: Symbolic value iteration, symbolic policy iteration, and a direct solution of the Bellman equation. The methods are illustrated on four nonlinear control problems: Velocity control under friction, one-link and two-link pendulum swing-up, and magnetic manipulation. The results show that the value functions yield well-performing policies and are compact, mathematically tractable, and easy to plug into other algorithms. This makes them potentially suitable for further analysis of the closed-loop system. A comparison with an alternative approach using neural networks shows that our method outperforms the neural network-based one. Learning & Autonomous Contro