PINNs

This course is designed to provide a deep understanding of Physics-Informed Neural Networks (PINNs) and their applications in the Healthcare & Life Sciences industries. Participants will learn how to integrate physical laws and domain knowledge into neural network models, enabling them to solve complex problems in biomechanics, physiological modeling, and drug delivery. The course covers the theoretical foundations of PINNs, as well as practical implementation strategies and case studies specific to the healthcare and life sciences domains.

• Understand the theoretical foundations and advantages of Physics-Informed Neural Networks

• Formulate and implement PINNs for solving PDEs relevant to the Healthcare & Life Sciences industries

• Incorporate domain knowledge and physical constraints into neural network architectures

• Apply PINNs to solve forward and inverse problems in biomechanics, physiological modeling, and drug delivery

• Evaluate and interpret the performance of PINN models using appropriate metrics and visualization techniques

1. Introduction to Physics-Informed Neural Networks

• Overview of PINNs and their advantages over traditional numerical methods

• Mathematical formulation of PINNs for solving PDEs

• Comparison of PINNs with other machine learning approaches (e.g., surrogate modeling, data-driven methods)

• Hands-on exercises: Implementing a basic PINN for solving a simple PDE in a biological context

2. PINNs for Biomechanics and Physiological Modeling

• Governing equations in biomechanics (e.g., elasticity, fluid-structure interaction)

• Formulating PINNs for soft tissue mechanics and cardiovascular modeling

• Incorporating material properties and boundary conditions into PINNs

• Hands-on exercises: Developing a PINN model for a simplified biomechanical or physiological problem

3. PINNs for Drug Delivery and Pharmacokinetics

• Governing equations in drug delivery (e.g., diffusion, advection, reaction)

• Formulating PINNs for drug transport in biological tissues

• Inverse problems and parameter estimation using PINNs

• Hands-on exercises: Implementing PINNs for a drug delivery or pharmacokinetic problem

4. Advanced Topics and Applications

• Uncertainty quantification and Bayesian neural networks

• Transfer learning and domain adaptation with PINNs

• Case studies of PINNs in the Healthcare & Life Sciences industries (e.g., personalized medicine, virtual surgery)

• Hands-on exercises: Applying PINNs to a real-world Healthcare or Life Sciences problem

• Strong understanding of partial differential equations (PDEs) and numerical methods

• Proficiency in programming with Python and deep learning frameworks (e.g., TensorFlow, PyTorch)

• Familiarity with fluid mechanics, biomechanics, and physiological modeling concepts