Physics-constrained machine learning for scientific computing
0In this talk, we discuss the development of physically-constrained machine learning (ML) models that incorporate techniques from scientific computing for learning dynamical and physical systems with applications in epidemiology and fluid dynamics. We first study the lack of generalization of black-box deep learning models for ODEs with applications to COVID-19 forecasting and the need for incorporation of advanced numerical integration schemes. We then focus on learning a physical model that satisfies conservation laws which are ubiquitous in science and engineering problems ranging from heat transfer to fluid flow. Violation of these well-known physical laws can lead to nonphysical solutions. To address this issue, we propose a framework, which constrains a pre-trained black-box ML model to satisfy conservation by enforcing the integral form from finite volume methods. We provide a detailed analysis of our method on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs that is used in groundwater flow. Our model maintains probabilistic uncertainty quantification (UQ), and deals well with shocks and heteroscedasticities. As a result, it achieves superior predictive performance on downstream tasks, e.g., shock location detection. Lastly, we study how to hard-constrain Neural Operator solutions to PDEs to satisfy the physical constraint of boundary conditions on a wide range of problems including Burgers’ and the Navier-Stokes’ equations. Our model improves the accuracy at the boundary and better guides the learning process on the interior of the domain. In summary, we demonstrate that carefully and properly enforcing physical constraints using techniques from numerical analysis results in better model accuracy and generalization in scientific applications. \n\nSpeakers:\nDanielle Maddix Robinson\nSenior Applied Scientist in the Machine Learning Forecasting Group\nAWS AI Labs\n\nModerators:\nMarkus Reichstein\nDirector & Professor\nMax Planck Institute for Biogeochemistry\n\nJoin the Neural Network!\nhttps://aiforgood.itu.int/neural-network/\nThe AI for Good networking community platform powered by AI. \nDesigned to help users build connections with innovators and experts, link innovative ideas with social impact opportunities, and bring the community together to advance the SDGs using AI.\n\n Watch the latest #AIforGood videos!\n\n\n Stay updated and join our weekly AI for Good newsletter:\nhttp://eepurl.com/gI2kJ5\n\nCheck out the latest AI for Good news:\nhttps://aiforgood.itu.int/newsroom/\n\nExplore the AI for Good blog:\nhttps://aiforgood.itu.int/ai-for-good-blog/\n\n Connect on our social media:\nWebsite: https://aiforgood.itu.int/\nTwitter: https://twitter.com/AIforGood\nLinkedIn Page: https://www.linkedin.com/company/26511907 \nLinkedIn Group: https://www.linkedin.com/groups/8567748 \nInstagram: https://www.instagram.com/aiforgood \nFacebook: https://www.facebook.com/AIforGood\n\nWhat is AI for Good?\nWe have less than 10 years to solve the UN SDGs and AI holds great promise to advance many of the sustainable development goals and targets.\nMore than a Summit, more than a movement, AI for Good is presented as a year round digital platform where AI innovators and problem owners learn, build and connect to help identify practical AI solutions to advance the United Nations Sustainable Development Goals.\nAI for Good is organized by ITU in partnership with 40 UN Sister Agencies and co-convened with Switzerland.\n\nDisclaimer:\nThe views and opinions expressed are those of the panelists and do not reflect the official policy of the ITU.