Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.

This research project investigates Lenia, an artificial life platform that simulates ecosystems of digital creatures. Lenia's ecosystem consists of simple, artificial organisms that can move, consume, grow, and reproduce. The platform is important as a tool for studying artificial life and evolution, as it provides a scalable and flexible environment for creating a diverse range of organisms with varying abilities and behaviors. Measuring complexity in Lenia is a key aspect of the study, which identifies the metrics for measuring long-term complex emerging behavior of rules, with the aim of evolving better Lenia behaviors which are yet not discovered. The Genetic Algorithm uses neighborhoods or kernels as genotype while keeping the rest of the parameters of Lenia as fixed, for example growth function, to produce different behaviors respective to the population and then measures fitness value to decide the complexity of the resulting behavior. First, we use Variation over Time as a fitness function where higher variance between the frames are rewarded. Second, we use Auto-encoder based fitness where variation of the list of reconstruction loss for the frames is rewarded. Third, we perform combined fitness where higher variation of the pixel density of reconstructed frames is rewarded. All three experiments are tweaked with pixel alive threshold and frames used. Finally, after performing nine experiments of each fitness for 500 generations, we pick configurations from all experiments such that there is a scope of further evolution, and run it for 2500 generations. Results show that the kernel's center of mass increases with a specific set of pixels and together with borders the kernel try to achieve a Gaussian distribution. Results are available at https://s4nyam.github.io/evolenia/

In this research, we investigate the possibility of applying a search strategy to genetic algorithms to explore the entire genetic tree structure. Several methods aid in performing tree searches; however, simpler algorithms such as breadth-first, depth-first, and iterative techniques are computation-heavy and often result in a long execution time. Adversarial techniques are often the preferred mechanism when performing a probabilistic search, yielding optimal results more quickly. The problem we are trying to tackle in this paper is the optimization of neural networks using genetic algorithms. Genetic algorithms (GA) form a tree of possible states and provide a mechanism for rewards via the fitness function. Monte Carlo Tree Search (MCTS) has proven to be an effective tree search strategy given states and rewards; therefore, we will combine these approaches to optimally search for the best result generated with genetic algorithms.

For example, a grid-based search is a classical approach for spacecraft preliminary trajectory design. However, this technique is more suitable for impulsive trajectory since the search space is much smaller. Due to the curse of dimensionality, low-thrust trajectory design often needs a more intelligent global search algorithm. Evolutionary algorithms, including Differential Evolution (DE) [4], Genetic algorithm (GA) [5], Particle swarm optimization (PSO) [6], etc., have been widely used in global optimization problems in spacecraft trajectory design [7, 8, 9, 10]. These algorithms iteratively generate new solutions by introducing randomness to previously obtained solutions and downselecting the solutions based on specific quality metrics. In addition, researchers also combine stochastic search algorithms with local gradient-based optimizers to attempt to find the globally optimal solution. The multistart method samples the search space with a fixed distribution and feeds the samples into a local optimizer as starting points for local search [10]. Inspired by energy minimization principles in computational chemistry, Monotonic Basin Hopping (MBH) [11, 12] adds random perturbations during the local search to uncover multiple local optima solutions that are close to each other. MBH rapidly became popular in the sphere of spacecraft trajectory design [1, 13, 14] and has been established as the state-of-the-art algorithm in terms of efficiency and solution quality through various benchmarks [15, 9, 10].

QDax is an open-source library with a streamlined and modular API for Quality-Diversity (QD) optimization algorithms in Jax. The library serves as a versatile tool for optimization purposes, ranging from black-box optimization to continuous control. QDax offers implementations of popular QD, Neuroevolution, and Reinforcement Learning (RL) algorithms, supported by various examples. All the implementations can be just-in-time compiled with Jax, facilitating efficient execution across multiple accelerators, including GPUs and TPUs. These implementations effectively demonstrate the framework's flexibility and user-friendliness, easing experimentation for research purposes. Furthermore, the library is thoroughly documented and tested with 95\% coverage.

Evolutionary algorithms (EAs) are increasingly being using in applications such as computer games [De Souza, 2014, Hastings et al., 2009] and robotics [Hoffmann, 2001, Fleming and Purshouse, 2002] to learn control algorithms (policies), as well as being applied to classic control tasks such as the benchmark suites available in OpenAi Gym [Brockman et al., 2016]. Often direct policy search algorithms such as EAs require a large number of evaluations: when these evaluations are costly in terms of time, this can result in extremely long learning times, which can be prohibitive in the worst case. Unfortunately many applications of interest suffer from this problem. For example, the protein folding problem [Dill et al., 2008] requires costly simulations, while applications that involve a double optimization process are also considered very computationally costly. This includes for example the joint optimization of robot morphology and control [Hart and Le Goff, 2022, Le Goff et al., 2021] in simulation (which typically use an outer loop to evolve body-plans and a nested inner-loop to evolve control), nested combinatorial optimization problems[Wu et al., 2021, Kobeaga et al., 2021] or hyperparameter optimization [De Souza et al., 2022]. Specifically in robotics, evaluations that need to be conducted directly on a physical robot to avoid any reality-gap tend to be very time-consuming, while repeating lengthy evaluations also places considerable wear and tear on machinery, potentially leading to unreliable objective-function values.

In this letter, we propose a model parameter identification method via a hyperparameter optimization scheme (MI-HPO). Our method adopts an efficient explore-exploit strategy to identify the parameters of dynamic models in a data-driven optimization manner. We utilize our method for model parameter identification of the AV-21, a full-scaled autonomous race vehicle. We then incorporate the optimized parameters for the design of model-based planning and control systems of our platform. In experiments, MI-HPO exhibits more than 13 times faster convergence than traditional parameter identification methods. Furthermore, the parametric models learned via MI-HPO demonstrate good fitness to the given datasets and show generalization ability in unseen dynamic scenarios. We further conduct extensive field tests to validate our model-based system, demonstrating stable obstacle avoidance and high-speed driving up to 217 km/h at the Indianapolis Motor Speedway and Las Vegas Motor Speedway. The source code for our work and videos of the tests are available at https://github.com/hynkis/MI-HPO.

Numerical methods for Inverse Kinematics (IK) employ iterative, linear approximations of the IK until the end-effector is brought from its initial pose to the desired final pose. These methods require the computation of the Jacobian of the Forward Kinematics (FK) and its inverse in the linear approximation of the IK. Despite all the successful implementations reported in the literature, Jacobian-based IK methods can still fail to preserve certain useful properties if an improper matrix inverse, e.g. Moore-Penrose (MP), is employed for incommensurate robotic systems. In this paper, we propose a systematic, robust and accurate numerical solution for the IK problem using the Mixed (MX) Generalized Inverse (GI) applied to any type of Jacobians (e.g., analytical, numerical or geometric) derived for any commensurate and incommensurate robot. This approach is robust to whether the system is under-determined (less than 6 DoF) or over-determined (more than 6 DoF). We investigate six robotics manipulators with various Degrees of Freedom (DoF) to demonstrate that commonly used GI's fail to guarantee the same system behaviors when the units are varied for incommensurate robotics manipulators. In addition, we evaluate the proposed methodology as a global IK solver and compare against well-known IK methods for redundant manipulators. Based on the experimental results, we conclude that the right choice of GI is crucial in preserving certain properties of the system (i.e. unit-consistency).

UELED by the surge in the collection of diverse data, coupled with advancements in computational models and models in the healthcare domain, they typically perform well algorithms, artificial intelligence (AI) techniques have been on a single task [16], [17]. Meta-learning models, however, striving to establish a strong foothold in healthcare over the prove beneficial both in multi-task scenarios, where taskagnostic past decade [1]-[3]. This burgeoning trend has fostered a knowledge is garnered from a suite of tasks to enhance growing interest in the deployment of innovative data analysis the learning of new tasks within that suite, and in singletask methods and machine learning (ML) techniques across a scenarios, where a single problem is continually solved range of healthcare applications [4]-[7]. As a specialized area and refined solutions for a single problem over numerous within ML, meta-learning, or learning-to-learn, has recently episodes [10], [18]. This multi-task learning capability can gained significant attention due to its impressive theoretical enable a more comprehensive understanding of the complex and practical advancements, making it a primary choice for interrelations and dependencies between various healthcare numerous applications [8]-[10].

Robots in 3D spaces with more than six degrees of freedom are redundant. A redundant robot allows multiple configurations of the robot for the given target point in the dexterous workspace. The presence of multiple solutions helps in resolving constraints in workspace such as object avoidance and energy minimization during trajectory planning. Inverse kinematics solutions of such redundant robotics are intricate. The present study involves comparison of different metaheuristic optimization algorithms (MOA), which have a positional error, and identify a MOA for high precision of positioning of the end effector of the robot. This study applies recent MOA for the inverse kinematics of hyper redundant nine degrees of freedom (DOF) robot arm by using forward kinematics of the Denavit-Hartenberg (DH) parameters and compares the performance of these algorithms. The comparative study shows Bald Eagle Search (BES) algorithm has better performance over other metaheuristic algorithms. BES algorithm outperforms the other MOA in achieving the desired position with very high precision and least positional error for a 9-DOF robot arm.