Accurate prediction of turbine blade fatigue life is essential for ensuring the safety and reliability of aircraft engines. A significant challenge in this domain is uncovering the intrinsic relationship between mechanical properties and fatigue life. This paper introduces Reinforced Symbolic Learning (RSL), a method that derives predictive formulas linking these properties to fatigue life. RSL incorporates logical constraints during symbolic optimization, ensuring that the generated formulas are both physically meaningful and interpretable. The optimization process is further enhanced using deep reinforcement learning, which efficiently guides the symbolic regression towards more accurate models. The proposed RSL method was evaluated on two turbine blade materials, GH4169 and TC4, to identify optimal fatigue life prediction models. When compared with six empirical formulas and five machine learning algorithms, RSL not only produces more interpretable formulas but also achieves superior or comparable predictive accuracy. Additionally, finite element simulations were conducted to assess mechanical properties at critical points on the blade, which were then used to predict fatigue life under various operating conditions.

Molecular optimization, which aims to discover improved molecules from a vast chemical search space, is a critical step in chemical development. Various artificial intelligence technologies have demonstrated high effectiveness and efficiency on molecular optimization tasks. However, few of these technologies focus on balancing property optimization with constraint satisfaction, making it difficult to obtain high-quality molecules that not only possess desirable properties but also meet various constraints. To address this issue, we propose a constrained multi-property molecular optimization framework (CMOMO), which is a flexible and efficient method to simultaneously optimize multiple molecular properties while satisfying several drug-like constraints. CMOMO improves multiple properties of molecules with constraints based on dynamic cooperative optimization, which dynamically handles the constraints across various scenarios. Besides, CMOMO evaluates multiple properties within discrete chemical spaces cooperatively with the evolution of molecules within an implicit molecular space to guide the evolutionary search. Experimental results show the superior performance of the proposed CMOMO over five state-of-the-art molecular optimization methods on two benchmark tasks of simultaneously optimizing multiple non-biological activity properties while satisfying two structural constraints. Furthermore, the practical applicability of CMOMO is verified on two practical tasks, where it identified a collection of candidate ligands of $\beta$2-adrenoceptor GPCR and candidate inhibitors of glycogen synthase kinase-3$\beta$ with high properties and under drug-like constraints.

In this paper, we present a novel approach for learning bimanual manipulation actions from human demonstration by extracting spatial constraints between affordance regions, termed affordance constraints, of the objects involved. Affordance regions are defined as object parts that provide interaction possibilities to an agent. For example, the bottom of a bottle affords the object to be placed on a surface, while its spout affords the contained liquid to be poured. We propose a novel approach to learn changes of affordance constraints in human demonstration to construct spatial bimanual action models representing object interactions. To exploit the information encoded in these spatial bimanual action models, we formulate an optimization problem to determine optimal object configurations across multiple execution keypoints while taking into account the initial scene, the learned affordance constraints, and the robot's kinematics. We evaluate the approach in simulation with two example tasks (pouring drinks and rolling dough) and compare three different definitions of affordance constraints: (i) component-wise distances between affordance regions in Cartesian space, (ii) component-wise distances between affordance regions in cylindrical space, and (iii) degrees of satisfaction of manually defined symbolic spatial affordance constraints.

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion from an optimization perspective. We formulate a series of constrained optimizations throughout the inference process of a diffusion model. In each optimization, we allow the sample to take multiple steps along the gradient of the proxy constraint function until we can no longer trust the proxy, according to the variance at each diffusion level. Additionally, we estimate the state manifold of diffusion model to allow for early termination when the sample starts to wander away from the state manifold at each diffusion step. Trust sampling effectively balances between following the unconditional diffusion model and adhering to the loss guidance, enabling more flexible and accurate constrained generation. We demonstrate the efficacy of our method through extensive experiments on complex tasks, and in drastically different domains of images and 3D motion generation, showing significant improvements over existing methods in terms of generation quality. Our implementation is available at https://github.com/will-s-h/trust-sampling.

Formulating an effective constraint model of a parameterised problem class is crucial to the efficiency with which instances of the class can subsequently be solved. It is difficult to know beforehand which of a set of candidate models will perform best in practice. This paper presents a system that employs graph rewriting to reformulate an input model for improved performance automatically. By situating our work in the Essence abstract constraint specification language, we can use the structure in its high level variable types to trigger rewrites directly. We implement our system via rewrite rules expressed in the Graph Programs 2 language, applied to the abstract syntax tree of an input specification. We show how to automatically translate the solution of the reformulated problem into a solution of the original problem for verification and presentation. We demonstrate the efficacy of our system with a detailed case study.

Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is viewed as a black box, the objective is to identify a small set of features that jointly determine the black box response with minimal error. However, finding such model-agnostic explanations is computationally demanding, as the problem is intractable even for binary classifiers. In this paper, the task is framed as a Constraint Optimization Problem, where the constraint solver seeks an explanation of minimum error and bounded size for an input data instance and a set of samples generated by the black box. From a theoretical perspective, this constraint programming approach offers PAC-style guarantees for the output explanation. We evaluate the approach empirically on various datasets and show that it statistically outperforms the state-of-the-art heuristic Anchors method.

However, although the cooperation between these two seems natural, the difference in their representation is obviously not negligible. Prof. Henry Kautz proposed a taxonomy of Neuro-Symbolic Systems in the AAAI 2020. In addition, many researchers have conducted relevant reviews of the recent neuro-symbolic AI from different perspectives. As Fig.1 shows, Acharya et al. [1] proposed a new classification method, which classified and discussed the application of existing neuro-symbolic AI by the role of neural and symbolic parts: learning for reasoning, reasoning for Learning, and learning-reasoning. Garcez et al. [73] proposed a taxonomy that includes sequential, nested, cooperative, and compiled neuro-symbolic AI based on the six types introduced by Henry Kautz. In addition, some reviews focus on cross-field integration and applications. For example, Berlot-Attwell [27] reviewed neuro-symbolic VQA (visual question answering) from the perspectives of AGI (artificial general intelligence) desiderata. Marra [128] conducted a comprehensive review on integrating neuro-symbolic and statistical relational artificial intelligence based on seven dimensions.

We present a framework for Multi-Robot Task Allocation (MRTA) in heterogeneous teams performing long-endurance missions in dynamic scenarios. Given the limited battery of robots, especially in the case of aerial vehicles, we allow for robot recharges and the possibility of fragmenting and/or relaying certain tasks. We also address tasks that must be performed by a coalition of robots in a coordinated manner. Given these features, we introduce a new class of heterogeneous MRTA problems which we analyze theoretically and optimally formulate as a Mixed-Integer Linear Program. We then contribute a heuristic algorithm to compute approximate solutions and integrate it into a mission planning and execution architecture capable of reacting to unexpected events by repairing or recomputing plans online. Our experimental results show the relevance of our newly formulated problem in a realistic use case for inspection with aerial robots. We assess the performance of our heuristic solver in comparison with other variants and with exact optimal solutions in small-scale scenarios. In addition, we evaluate the ability of our replanning framework to repair plans online.

Procedurally generated levels created by machine learning models can be unsolvable without further editing. Various methods have been developed to automatically repair these levels by enforcing hard constraints during the post-processing step. However, as levels increase in size, these constraint-based repairs become increasingly slow. This paper proposes using explainability methods to identify specific regions of a level that contribute to its unsolvability. By assigning higher weights to these regions, constraint-based solvers can prioritize these problematic areas, enabling more efficient repairs. Our results, tested across three games, demonstrate that this approach can help to repair procedurally generated levels faster.

Reductions are the fundamental tool of computational complexity. They allow classification of computational problems into families (somewhat resembling those in biology), with problems in the same class sharing common features (in particular NP-complete problems being isomorphic versions of a single problem, if we believe that the Berman-Hartmanis conjecture [6] holds). A significant concern in the literature on complexity-theoretic reductions is to make the theory of reductions more predictive. This means that we should aim to better connect the structural properties of the two problems that the given reduction is connecting. For instance the notion of pasimonious reduction attempts to preserve the total number of solutions between instances.