APMA-2070 and ENGN 2912: Deep Learning for Scientistis and Engineers

The main objective of this course is to teach concepts and implementation of deep learning techniques for scientific and engineering problems to first year graduate students. This course entails various methods, including theory and implementation of deep leaning techniques to solve a broad range of computational problems frequently encountered in solid mechanics, fluid mechanics, non destructive evaluation of materials, systems biology, chemistry, and non-linear dynamics.

Workload

Over the 13 weeks of this course (including reading period), students will spend three hours in class per week (39 hours total). A reasonable estimate to support this course’s learning outcomes is 180 hours total. Project based homework assignments may take ~60 hours, and students are expected to allocate ~80 hours to the final project.

Why this course

Please read through this

• Top 10 People in ML to follow in 2023 

Instructors

1. Prof. George Em Karniadakis, Division of Applied Mathematics, Brown University
2. Dr. Khemraj Shukla, Division of Applied Mathematics, Brown University

Syllabus, Lectures and Codes

Textbook and Other Reading Materials

• Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville 

• Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow by Auréliean Géron

• Conceptual Programming with Python by Thorsten Altenkirch and Isaac Triguero

Learning curve

Module I: Basics

Lecture 1 : Introduction Slides: (Jan 25,2023)
No Homework

Lecture 2 : A primer on Python, NumPy, SciPy and jupyter notebooks Slides: (Jan 25, 2023) Jupyter Notebook
Homework_L2 Due Date: 2/1/2023, 11:59 PM ET

Lecture 3: Deep Learning Networks Slides: (Feb 1, 2023) Jupyter Notebook
Homework_L3 Due Date: 3/01/2023, 11:59 PM ET

Lecture 4: A primer on TensorFlow, PyTorch and JAX Slides: (Feb 8, Feb 15, 2023) Jupyter_Notebook
Homework_L4 Due Date: 3/19/2023, 11:59 PM ET

Lecture 5: Training and Optimization Slides: (Feb 15, Feb 22, 2023) Jupyter_Notebook
Homework_L5 Due Date: 4/30/2023, 11:59 PM ET

Lecture 6: Neural Network Architectures Slides: (Feb 22, March 1, 2023) Jupyter_Notebook
Homework_L6 Due Date: 4/30/2023, 11:59 PM ET

end_of_semester_FUN_homework Due Date: 4/30/2023

Module II: Neural Differential Equations

Lecture 7: Discovering Differential Equations Slides: (March 8, 2023) Jupyter_Notebook

Lecture 8: Physics-Informed Neural Networks (PINNs)- Part I Slides: (March 15, March 22, 2023) Jupyter_Notebook

Lecture 9: Physics-Informed Neural Networks (PINNs)- Part II Slides: (March 22, 2023)

Module III: Neural Operators

Lecture 10: Deep Operator Network (DeepONet) Slides: (April 5, 2023) Jupyter_Notebook DATA_FOR_FNO
ADD_ON:FOURIER_REVIEW Jupyter_Notebook_Fourier

Lecture 11: Implementation of PINNs and DeepOnet Slides: (April 12, 2023) Video Jupyter_Notebook DATA_FOR_DEEPONET

Module IV: SciML Uncertainty Quantification (SciML-UQ)

Lecture 12: Machine Learning using Multi-Fidelity Data Slides: (April 19, April 26, 2023) Jupyter_Notebook

Lecture 13: Uncertainty Quantification(UQ) in Scientific Machine Learning Slides: (April 26, May 3, 2023) Jupyter_Notebook Slides: Neural_UQ Neural_UQ_PT_MODEL DATA_Neural_UQ

Advanced Topics

1. Multi-GPU Scientific Machine Learning Slides: (April 12, April 19, 2023) Python Code Slides: NVIDIA-MODULUS

Office hours

Monday 3:00 - 5:30 PM, Location: 170 Hope St., Room No: 308, Providence RI 02906

Project list

Term Projects

1. Biomedicine

   • Solving forward and inverse problems in mathematical modeling of blood coagulation: Project Files
   • Predicting drug absorption using a physics-informed neural network: Project Files
   • Parameter identification in Glucose-Insulin interaction: Project Files
   • Parameter Estimation in Thrombus Formation: Project Files

2. Dynamical Systems

   • Charged particle in a electromagnetic field: Project Files
   • Learning dynamical systems from data: Project Files
   • Stiff ODE systems: Project Files

3. Engines

   • Learning engine parameters: Project Files

4. Fluid Mechanics

   • Compute and benchmark the solution of Boussinesq Equation using different activation functions: Project Files
   • Modeling Bubble Growth Dynamics: Project Files
   • Reconstruction of flow past a cylinder: Project Files
   • Reconstruction of flow field for a lid driven cavity flow: Project Files
   • Solving forward and inverse problems in mathematical modeling of wave propagation: Project Files

5. Geophysics

   • Diffusion-Reaction in porous media: Project Files
   • Estimating sea-surface temperature using multi-fidelity data: Project Files
   • Microseismic hypocenter localization using PINNs: Project Files

6. Heat Transfer

   • Inverse heat transfer problem: Project Files
   • Steady state non-linear inverse heat conduction problem: Project Files
   • Heat Conduction in Double Layered Structures exposed to Ultra-short Pulsed Laser: Project Files
   • Benchmarking Finite-difference vs Automatic-Differetiation for steady-state PDEs: Project Files

7. Materials

   • Inverse Problem on Modulus Identification of Hyperelastic Material: Project Files
   • Characterizing surface breaking crack using ultrasound data and PINNs: Project Files