Recent technological advances have expanded the availability of high-throughput biological datasets, enabling the reliable design of digital twins of biomedical systems or patients. Such computational tools represent key reaction networks driving perturbation or drug response and can guide drug discovery and personalized therapeutics. Yet, their development still relies on laborious data integration by the human modeler, so that automated approaches are critically needed. The success of data-driven system discovery in Physics, rooted in clean datasets and well-defined governing laws, has fueled interest in applying similar techniques in Biology, which presents unique challenges. Here, we reviewed methodologies for automatically inferring digital twins from biological time series, which mostly involve symbolic or sparse regression. We evaluate algorithms according to eight biological and methodological challenges, associated to noisy/incomplete data, multiple conditions, prior knowledge integration, latent variables, high dimensionality, unobserved variable derivatives, candidate library design, and uncertainty quantification. Upon these criteria, sparse regression generally outperformed symbolic regression, particularly when using Bayesian frameworks. We further highlight the emerging role of deep learning and large language models, which enable innovative prior knowledge integration, though the reliability and consistency of such approaches must be improved. While no single method addresses all challenges, we argue that progress in learning digital twins will come from hybrid and modular frameworks combining chemical reaction network-based mechanistic grounding, Bayesian uncertainty quantification, and the generative and knowledge integration capacities of deep learning. To support their development, we further propose a benchmarking framework to evaluate methods across all challenges.

Reliable indoor navigation remains a significant challenge in complex environments, particularly where external positioning signals and dedicated infrastructures are unavailable. This research presents Grid2Guide, a hybrid navigation framework that combines the A* search algorithm with a Small Language Model (SLM) to generate clear, human-readable route instructions. The framework first conducts a binary occupancy matrix from a given indoor map. Using this matrix, the A* algorithm computes the optimal path between origin and destination, producing concise textual navigation steps. These steps are then transformed into natural language instructions by the SLM, enhancing interpretability for end users. Experimental evaluations across various indoor scenarios demonstrate the method's effectiveness in producing accurate and timely navigation guidance. The results validate the proposed approach as a lightweight, infrastructure-free solution for real-time indoor navigation support.

Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space but these may not be admissible throughout the domain thereby affecting the optimality guarantees of the search. Bounded suboptimal search using several such partially good but inadmissible heuristics was developed in Multi-Heuristic A* (MHA*). Although MHA* leverages multiple inadmissible heuristics to potentially generate a faster suboptimal solution, the original version does not improve the solution over time. It is a one shot algorithm that requires careful setting of inflation factors to obtain a desired one time solution. In this work, we tackle this issue by extending MHA* to an anytime version that finds a feasible suboptimal solution quickly and continually improves it until time runs out. Our work is inspired from the Anytime Repairing A* (ARA*) algorithm. We prove that our precise adaptation of ARA* concepts in the MHA* framework preserves the original suboptimal and completeness guarantees and enhances MHA* to perform in an anytime fashion. Furthermore, we report the performance of A-MHA* in 3-D path planning domain and sliding tiles puzzle and compare against MHA* and other anytime algorithms.

Path planning in robotics often involves solving continuously valued, high-dimensional problems. Popular informed approaches include graph-based searches, such as A*, and sampling-based methods, such as Informed RRT*, which utilize informed set and anytime strategies to expedite path optimization incrementally. Informed sampling-based planners define informed sets as subsets of the problem domain based on the current best solution cost. However, when no solution is found, these planners re-sample and explore the entire configuration space, which is time-consuming and computationally expensive. This article introduces Multi-Informed Trees (MIT*), a novel planner that constructs estimated informed sets based on prior admissible solution costs before finding the initial solution, thereby accelerating the initial convergence rate. Moreover, MIT* employs an adaptive sampler that dynamically adjusts the sampling strategy based on the exploration process. Furthermore, MIT* utilizes length-related adaptive sparse collision checks to guide lazy reverse search. These features enhance path cost efficiency and computation times while ensuring high success rates in confined scenarios. Through a series of simulations and real-world experiments, it is confirmed that MIT* outperforms existing single-query, sampling-based planners for problems in R^4 to R^16 and has been successfully applied to real-world robot manipulation tasks. A video showcasing our experimental results is available at: https://youtu.be/30RsBIdexTU

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug discovery. Indeed, they are desirable since they can adaptively gather information to make better decisions in the future, resulting in data-efficient workflows. In scientific discovery, where experiments are costly, these algorithms can thus significantly reduce the cost of experimentation. Theoretical analyses of these algorithms are crucial for understanding their behavior and providing valuable insights for developing next-generation algorithms. However, theoretical analyses in the literature are often inaccessible to non-experts. This monograph aims to provide an accessible, self-contained introduction to the theoretical analysis of commonly used probabilistic decision-making algorithms, including bandit algorithms, Bayesian optimization, and tree search algorithms. Only basic knowledge of probability theory and statistics, along with some elementary knowledge about Gaussian processes, is assumed.

Path planning for autonomous robots presents a fundamental trade-off between optimality and safety. While conventional algorithms typically prioritize one of these objectives, we introduce the Unified Path Planner (UPP), a unified framework that simultaneously addresses both. UPP is a graph-search-based algorithm that employs a modified heuristic function incorporating a dynamic safety cost, enabling an adaptive balance between path length and obstacle clearance. We establish theoretical sub-optimality bounds for the planner and demonstrate that its safety-to-optimality ratio can be tuned via adjustable parameters, with a trade-off in computational complexity. Extensive simulations show that UPP achieves a high success rate, generating near-optimal paths with only a negligible increase in cost over traditional A*, while ensuring safety margins that closely approach those of the classical Voronoi planner. Finally, the practical efficacy of UPP is validated through a hardware implementation on a TurtleBot, confirming its ability to navigate cluttered environments by generating safe, sub-optimal paths.

Enabling robots to efficiently search for and identify objects in complex, unstructured environments is critical for diverse applications ranging from household assistance to industrial automation. However, traditional scene representations typically capture only static semantics and lack interpretable contextual reasoning, limiting their ability to guide object search in completely unfamiliar settings. To address this challenge, we propose a language-enhanced hierarchical navigation framework that tightly integrates semantic perception and spatial reasoning. Our method, Goal-Oriented Dynamically Heuristic-Guided Hierarchical Search (GODHS), leverages large language models (LLMs) to infer scene semantics and guide the search process through a multi-level decision hierarchy. Reliability in reasoning is achieved through the use of structured prompts and logical constraints applied at each stage of the hierarchy. For the specific challenges of mobile manipulation, we introduce a heuristic-based motion planner that combines polar angle sorting with distance prioritization to efficiently generate exploration paths. Comprehensive evaluations in Isaac Sim demonstrate the feasibility of our framework, showing that GODHS can locate target objects with higher search efficiency compared to conventional, non-semantic search strategies. Website and Video are available at: https://drapandiger.github.io/GODHS

Monte Carlo Tree Search is a popular method for solving decision making problems. Faster implementations allow for more simulations within the same wall clock time, directly improving search performance. To this end, we present an alternative array-based implementation of the classic Upper Confidence bounds applied to Trees algorithm. Our method preserves the logic of the original algorithm, but eliminates the need for branch prediction, enabling faster performance on pipelined processors, and up to a factor of 2.8 times better scaling with search depth in our numerical simulations.

Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's properties, showing that minimizing the size of its search tree guided by ranked branching decisions is closely related to the Multi-armed bandit (MAB) problem. Building on this insight, MAB reinforcement learning algorithms are applied to FDS, extended with problem-specific refinements and parameter tuning, and evaluated on the two most fundamental scheduling problems, the Job Shop Scheduling Problem (JSSP) and Resource-Constrained Project Scheduling Problem (RCPSP). The resulting enhanced FDS, using the best extended MAB algorithm and configuration, performs 1.7 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks compared to the original implementation in a new solver called OptalCP, while also being 3.5 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks than the current state-of-the-art FDS algorithm in IBM CP Optimizer 22.1. Furthermore, using only a 900-second time limit per instance, the enhanced FDS improved the existing state-of-the-art lower bounds of 78 of 84 JSSP and 226 of 393 RCPSP standard open benchmark instances while also completely closing a few of them.

Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the asymmetric bidirectional search due to the limitations of lazy-reverse search. To address this challenge, we propose Greedy GuILD Grafting Trees (G3T*), a novel path planner that grafts invalid edge connections at both ends to re-establish tree-based connectivity, enabling rapid path convergence. G3T* employs a greedy approach using the minimum Lebesgue measure of guided incremental local densification (GuILD) subsets to optimize paths efficiently. Furthermore, G3T* dynamically adjusts the sampling distribution between the informed set and GuILD subsets based on historical and current cost improvements, ensuring asymptotic optimality. These features enhance the forward search's growth towards the reverse tree, achieving faster convergence and lower solution costs. Benchmark experiments across dimensions from R^2 to R^8 and real-world robotic evaluations demonstrate G3T*'s superior performance compared to existing single-query sampling-based planners. A video showcasing our experimental results is available at: https://youtu.be/3mfCRL5SQIU