相关论文: Generating Triangulations and Fibrations with Rein…
Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth Calabi-Yau threefolds. We introduce CYTransformer, a deep…
The design of materials structure for optimizing functional properties and potentially, the discovery of novel behaviors is a keystone problem in materials science. In many cases microstructural models underpinning materials functionality…
Autonomous manipulation of granular media, such as sand, is crucial for applications in construction, excavation, and additive manufacturing. However, shaping granular materials presents unique challenges due to their high-dimensional…
Calabi-Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our…
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3…
We use reinforcement learning as a means of constructing string compactifications with prescribed properties. Specifically, we study heterotic SO(10) GUT models on Calabi-Yau three-folds with monad bundles, in search of phenomenologically…
We study the birational geometry (i.e., K\"ahler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes…
We provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an upper bound on the number of Calabi-Yau threefold…
Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the…
We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batyrev's construction. We demonstrate that such algorithms efficiently optimize physical…
Excavation of irregular rigid objects in clutter, such as fragmented rocks and wood blocks, is very challenging due to their complex interaction dynamics and highly variable geometries. In this paper, we adopt reinforcement learning (RL) to…
One may construct a large class of Calabi-Yau varieties by taking anticanonical hypersurfaces in toric varieties obtained from reflexive polytopes. If the intersection of a reflexive polytope with a hyperplane through the origin yields a…
Advancements in additive manufacturing have enabled design and fabrication of materials and structures not previously realizable. In particular, the design space of composite materials and structures has vastly expanded, and the resulting…
Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi-Yau hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed polytopes with a minimal number of facets and of inscribed…
Deep Learning has become overly complicated and has enjoyed stellar success in solving several classical problems like image classification, object detection, etc. Several methods for explaining these decisions have been proposed. Black-box…
We investigate reinforcement learning and genetic algorithms in the context of heterotic Calabi-Yau models with monad bundles. Both methods are found to be highly efficient in identifying phenomenologically attractive three-family models,…
We introduce TriSearch, a reinforcement learning framework for optimizing objectives over triangulations of a polytope via bistellar flips. The key idea is a circuit-supported subtriangulation action representation: feasible flips are…
Flexibility design problems are a class of problems that appear in strategic decision-making across industries, where the objective is to design a ($e.g.$, manufacturing) network that affords flexibility and adaptivity. The underlying…
In reinforcement learning (RL), it is easier to solve a task if given a good representation. While deep RL should automatically acquire such good representations, prior work often finds that learning representations in an end-to-end fashion…
Recent advances at the intersection of reinforcement learning (RL) and visual intelligence have enabled agents that not only perceive complex visual scenes but also reason, generate, and act within them. This survey offers a critical and…