ETH Zürich AISE: Physics-Informed Neural Networks – Limitations and Extensions Part 2

↓↓↓ LECTURE OVERVIEW BELOW ↓↓↓ ETH Zürich AI in the Sciences and Engineering 2024 *Course Website* (links to slides and tutorials): https://www.camlab.ethz.ch/teaching/ai-in-the-sciences-and-engineering-2024.html Lecturers: Dr. Ben Moseley and Prof. Siddhartha Mishra ▬ Lecture Content ▬▬▬ 0:00 - Recap: previous lecture 7:10 - Poor convergence of PINNs 10:29 - Using hard constraints for PINNs 18:51 - Adaptive loss terms 22:47 - Adaptive collocation points 26:36 - Scaling to complex problems 33:24 - Fourier input features 38:54 - Combining PINNs with domain decomposition 42:58 - Finite basis PINNs 55:06 - Other PINN extensions 58:25 - Bayesian PINNs 1:04:14 - Custom network architectures ▬ Course Overview ▬▬▬ Lecture 1: Course Introduction youtube.com/watch?v=LkKvhvsf6jY&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 2: Introduction to Deep Learning Part 1 youtube.com/watch?v=OXmLwCQA7F4&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 3: Introduction to Deep Learning Part 2 youtube.com/watch?v=z3tQaNOwQqM&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 4: Importance of PDEs in Science youtube.com/watch?v=UiZxDRBd0Q8&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 5: Physics-Informed Neural Networks – Introduction youtube.com/watch?v=D-F7BYRhAkQ&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 6: Physics-Informed Neural Networks – Limitations and Extensions Part 1 youtube.com/watch?v=S11QK8baGVI&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 7: Physics-Informed Neural Networks – Limitations and Extensions Part 2 youtube.com/watch?v=NFtE1pyD5LA&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 8: Physics-Informed Neural Networks – Theory Part 1 youtube.com/watch?v=AaChPylEH6U&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 9: Physics-Informed Neural Networks – Theory Part 2 youtube.com/watch?v=FqdJ2Jx9MVc&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 10: Introduction to Operator Learning Part 1 youtube.com/watch?v=yhHhMmiNl_g&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 11: Introduction to Operator Learning Part 2 youtube.com/watch?v=lEUgPvDi5O8&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 12: Fourier Neural Operators youtube.com/watch?v=b96wRdjH1Lg&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 13: Spectral Neural Operators and Deep Operator Networks youtube.com/watch?v=BxklDO0TMlA&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 14: Convolutional Neural Operators youtube.com/watch?v=5XaLKR08TwI&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 15: Time-Dependent Neural Operators youtube.com/watch?v=u1KFcAvjyCI&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 16: Large-Scale Neural Operators youtube.com/watch?v=FPXW9MxjV48&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 17: Attention as a Neural Operator youtube.com/watch?v=wJSgLRiU7D4&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 18: Windowed Attention and Scaling Laws youtube.com/watch?v=YtJhReM5bHY&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 19: Introduction to Hybrid Workflows Part 1 youtube.com/watch?v=fJbt6VKYycA&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 20: Introduction to Hybrid Workflows Part 2 youtube.com/watch?v=h8BH-6tjecc&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 21: Neural Differential Equations youtube.com/watch?v=jnjYsm4NjhE&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 22: Introduction to Diffusion Models youtube.com/watch?v=Tohlijxz3XQ&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 23: Introduction to JAX youtube.com/watch?v=0JsPcm_Vl1g&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 24: Symbolic Regression and Model Discovery youtube.com/watch?v=fe-PC4lw4yw&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 25: Applications of AI in Chemistry and Biology Part 1 youtube.com/watch?v=Y3rvzsW8TVU&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r Lecture 26: Applications of AI in Chemistry and Biology Part 2 youtube.com/watch?v=dDvTA_MoO_4&list=PLJkYEExhe7rYFkBIB2U5pf_RWzYnFLj7r ▬ Course Description ▬▬▬ AI is having a profound impact on science by accelerating discoveries across physics, chemistry, biology, and engineering. This course presents a highly topical selection of AI applications across these fields. Emphasis is placed on using AI, particularly deep learning, to understand systems modelled by PDEs, and key scientific machine learning concepts and themes are discussed. ▬ Course Learning Objectives ▬▬▬ - Aware of advanced applications of AI in the sciences and engineering - Familiar with the design, implementation, and theory of these algorithms - Understand the pros/cons of using AI and deep learning for science - Understand key scientific machine learning concepts and themes