FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.Comment: 44 page

Prédictions de la stabilité et des propriétés électroniques de phases Heusler quaternaires par apprentissage automatique

National audienc

Screening quaternary Heusler by machine learning for application in thermoelectricity

International audienc

Screening quaternary Heusler by machine learning for application in thermoelectricity

International audienceHeusler alloys, full and half-, thanks to their high versatility of compositions as well as their very interesting properties, are good candidates for thermoelectric applications. In the Heusler family, quaternary alloys also exist and allow to further increase the chemical diversity and so one to achieve more complex properties. However, due to the high number of combinations, traditional screening methods are not effective to target relevant compounds. To accelerate this research, it is advantageous to use machine learning methods. In our project, we are looking for new promising quaternary Heusler compounds screened within a dataset of 24 selected elements. First, a database of calculated thermodynamic, electronic and magnetic properties, obtain from DFT calculations (Density Functional Theory) on binary and ternary compounds was constructed. Then, a supervised learning with the neural network model was built to predict the enthalpy of formation and the density of state at the Fermi level (metallic or semiconductor character) of quaternary Heusler compounds. Our model presents comparable or superior performance than the state of art and allow to identify promising compounds among the 24^4 possible configurations of our dataset

Two-dimensional nanofluidics for blue energy harvesting

Blue energy harvesting based on the ion flow obtained from seas and rivers provides a clean, stable and continuous electric output that is highly dependent on ion-selective membranes (ISMs) that conduct single ions. In recent years, ISMs constructed based on two-dimensional (2D) nanofluidics have demonstrated promising application prospects in blue energy harvesting due to their facile fabrication, excellent ion selectivity and high ion flux. In this review, the principles of 2D nanofluidics in regulating ionic transport are firstly proposed and discussed, including ion selectivity and ultrafast ion transmission, which are considered as two critical factors for achieving highly efficient blue energy harvesting. The advantages of 2D nanofluidics towards blue energy harvesting are analyzed to reveal the necessity of this review. The construction of 2D nanofluidic membranes based on several typical materials and their recent research advances in salinity gradient- and pressure-driven blue energy harvesting are also summarized in detail. Finally, the existing challenges of 2D nanofluidic membranes regarding blue energy harvesting applications are discussed to provide new insights for the development of high-performance blue energy harvesting systems based on 2D nanofluidics