AI-based Learning for Physical Simulation

Información del proyecto

ALPS

Identificador del acuerdo de subvención: 101039481

DOI

10.3030/101039481

Fecha de la firma de la CE 31 Mayo 2022

Fecha de inicio 1 Septiembre 2022

Fecha de finalización 31 Agosto 2027

Financiado con arreglo a

• European Research Council (ERC)

Coste total

€ 1 315 000,00

Aportación de la UE

€ 1 315 000,00

Coordinado por

AARHUS UNIVERSITET
Denmark

Periodic Reporting for period 1 - ALPS (AI-based Learning for Physical Simulation)

Período documentado: 2022-09-01 hasta 2025-02-28

Resumen del contexto y de los objetivos generales del proyecto

Computer simulations are widely used in both scientific research and engineering today. While access to large datasets has led to the growing use of Artificial Intelligence (AI) and Machine Learning (ML) to enhance these simulations, there are some challenges with purely data-driven models. These models often struggle to make accurate predictions in new, unseen situations (a concept known as generalization) and are often seen as “black boxes,” meaning their inner workings are hard to understand. This lack of transparency can be a barrier to scientific progress and makes it difficult for researchers to assess their reliability and safety, which is especially important in fields involving ethical concerns.

To address these issues, we are developing a hybrid approach that blends ML techniques with traditional mathematical modeling. This will help improve the model’s ability to generalize, especially when there is limited data available, while also ensuring that the models remain interpretable by humans. A key feature of our approach is the development of algorithms that can derive simple mathematical equations from data. These general-purpose methods and algorithms will be applied to various fields, including robotics, fluid mechanics, and the modeling of complex materials.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

In the first part of the project, we have introduced a new framework that uses a discrete mathematical theory and evolutionary algorithms to derive models starting from data. The mathematical theory, called discrete exterior calculus, provides a set of concepts that can be used as building blocks to model a wide range of physical phenomena. The evolutionary algorithm searches the space of possible models by combining the building blocks according to specific rules (like the grammar of a language) and producing a population of many candidate equations. The models evolve through “mutation”, “mating” and “selection of the fittest”, replicating natural processes. We have implemented this framework in an open-source software library and demonstrated that it is able to recover equations of many physical systems that state-of-the-art symbolic regression algorithms struggle to discover. We are currently improving the effectiveness of our algorithms using modern high-performance computing techniques and developing smarter search strategies. We have also started applying our methods in several fields including the development of new accurate and interpretable models for simulating fluid and traffic flows.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

Our findings could have a significant impact across many fields, including economics, where the demand for clear and understandable knowledge is increasing. By integrating humans into the modeling process using AI and ML, researchers and engineers can gain valuable insights into how complex systems work. Additionally, combining mathematical symbols with AI may lead to a paradigm shift in the field towards neuro-symbolic models—hybrid models that could offer better generalization than current methods. Further investigation is needed to explore the potential and effectiveness of these neuro-symbolic models. Ultimately, as a part of the high gains of the project, we expect our approach to contribute to the development of a safe and transparent AI.