APMA2070_S2025

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# APMA-2070: Deep Learning for Scientistis and Engineers: Spring 2025

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  ](https://academy.digilab.co.uk/posts/which-ml-experts-should-you-follow-in-2023)

# Instructors  
[Dr. Khemraj Shukla, Division of Applied Mathematics, Brown University](https://scholar.google.com/citations?user=XMWXf8sAAAAJ&hl=en&oi=ao)

Dr. Khemraj Shukla: Friday: 3.00 PM - 5.30 PM 
Room No: 308 
Division of Applied Mathematics 
170 Hope St 
Providence RI 02906 
Email: <khemraj_shukla@brown.edu>

# TAs
Aniruddha Bora 
Email: <aniruddha_bora@brown.edu>

# Syllabus, Lectures and Codes

**Textbook and Other Reading Materials**

* [ Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville  ](https://www.deeplearningbook.org)

* [ Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow by Auréliean Géron ](https://www.amazon.com/Hands-Machine-Learning-Scikit-Learn-TensorFlow/dp/1492032646)

* [ Conceptual Programming with Python by Thorsten Altenkirch and Isaac Triguero ](https://www.google.com/books/edition/Conceptual_Programming_with_Python/nUO0DwAAQBAJ?hl=en&gbpv=1&dq=conceptual+programming+with+python&printsec=frontcover)

* [ A Student's Guide to Bayesian Statistics by B Lambert ](https://www.torrossa.com/en/resources/an/5017731)

* [ Reinforcement learning: An Introduction, 2nd edition by Richard S Sutton and Andrew G Barto ](https://scholar.google.ca/citations?view_op=view_citation&hl=en&user=6m4wv6gAAAAJ&citation_for_view=6m4wv6gAAAAJ:IWHjjKOFINEC)

**Learning curve**
![Learning curve](https://raw.githubusercontent.com/raj-brown/APMA2070_S2025/main/images/learning_curve.png)

## Office Hours
Every Friday: 3:00 PM - 5.30 PM   
Room No: 118  
1st Floor, Division of Applied Mathematics   
170 Hope St   
Providence RI 02906

## Module I: Basics

**Lecture 1 : Introduction** [Slides: (Jan 27,2025)](https://www.dropbox.com/scl/fi/zjc8fx44mb6z78a67kiw8/Lecture_01_Introduction.pptx?rlkey=b8kkgall360i9taaide0jbf6z&st=hd5pjyzb&dl=0)  
[Homework\_L1](Homeworks/HW\_L1.pdf) Due Date: 2/10/2025, 11:59 PM ET

**Lecture 2 : A primer on Python, NumPy, SciPy, jupyter notebooks and MATLAB** [Slides: (Feb 3, 2025)](https://www.dropbox.com/scl/fi/xafih1gn97ggfdao1nt6c/Lecture_02_Primer_Python_Final.pptx?rlkey=ms1j3gkiu14vmx8re6zzckvq0&st=8mtthpiz&dl=0) [Jupyter Notebook](https://github.com/raj-brown/APMA2070_S2025/blob/main/Lecture_2_Notebook/Python_Codes/python_primer.ipynb) [MATLAB_Codes](https://github.com/raj-brown/APMA2070_S2025/blob/main/Lecture_2_Notebook/MATLAB_Codes/poisson_pde_fem.m)  
[Homework\_L2](Homeworks/HW\_L2.pdf) Due Date: 2/24/2025, 11:59 PM ET

**Lecture 3: Deep Learning Networks** [Slides: (Feb 3, Feb 10, 2025)](https://www.dropbox.com/scl/fi/3bph2sv53jrnbzi95ebh8/Lecture_03_Deep_Neural_Networks.pptx?rlkey=d93sa6ed4guc15etku2pjirfb&dl=0) [Jupyter Notebook](https://github.com/raj-brown/APMA2070_S2025/blob/main/Lecture_3_Notebook/Python_Code/lec_03.ipynb) [MATLAB_Codes](https://github.com/raj-brown/APMA2070_S2025/blob/main/Lecture_3_Notebook/MATLAB_CODES/driver.m)
[Homework\_L3](Homeworks/HW\_L3.pdf) Due Date: 3/10/2025, 11:59 PM ET

**Lecture 4: A primer on TensorFlow, PyTorch, JAX and MATLAB** [Slides: (Feb 24, 2025)](https://www.dropbox.com/scl/fi/wq22gbfblu10e9kfgyxm2/Lecture_04_Primer_PyT_TF_JAX.pptx?rlkey=l4egneb7gw82m5x76378jhax3&st=edoxqb9o&dl=0) [Jupyter\_Notebook](Lecture_4_Notebook/Python_Codes/1-pytorch.ipynb) [MATLAB_Codes](Lecture_4_Notebook/MATLAB_Codes/matlabDLbasic.m)  
[Homework\_L4](Homeworks/HW\_L4.pdf) Due Date: 03/24/2025, 11:59 PM ET

**Lecture 5: Training and Optimization** [Slides: (March 3, 2025)](https://www.dropbox.com/scl/fi/ftcfkxn4htyd9j9t10vxk/Lecture_05_Training_and_Optimization.pptx?rlkey=tlvjo3m5ljtbs6pewqaeyfu83&dl=0) [Jupyter\_Notebook](Lecture_5_Notebook/Python_Codes/optimizer_00.ipynb)  
[Homework\_L5](Homeworks/HW\_L5.pdf) [STARTING\_CODE](Homeworks/HW\_5\_CODE)  Due Date: 4/07/2025, 11:59 PM ET

**Lecture 6: Neural Network Architectures** [Slides: (March 10, 2024)](https://www.dropbox.com/scl/fi/ysrirwvzphpxj2wn101sh/Lecture_06_NN_Architectures.pptx?rlkey=qebql65ntpk3iw08qex7so4wj&st=6hgskcjx&dl=0) [Jupyter\_Notebook](Lecture_6_Notebook/nn_architectures.ipynb)  
[Homework\_L6](Homeworks/HW\_L6.pdf) Due Date: 4/28/2025, 11:59 PM ET

## Module II: Neural Differential Equations

**Lecture 7a: Discovering Differential Equations** [Slides: (March 17, 2024)](https://www.dropbox.com/scl/fi/p2zzsg7okayw00t8qmwqc/Lecture-7a-Dynamical-systems.pptx?rlkey=q0jns6kze63zrl32srrkiwd9q&dl=0) [Jupyter\_Notebook](Lecture_7a_Notebook/dynSys.ipynb)

**Lecture 7b: Distillation of Neural Networks** [Slides: (March 31, 2025)](https://www.dropbox.com/scl/fi/fvtw25vvbm2b2zczejz23/Lecture-7b-Distillation-of-Neural_Networks.pptx?rlkey=s9zjfjre8y5qyx8zvlwd8fs3r&st=7uwbzoto&dl=0) [Jupyter\_Notebook](Lecture_7b_Notebook/pysr.ipynb)

**Lecture 8: Physics-Informed Neural Networks (PINNs)- Part I** [Slides: (March 31, April 7, 2025)](https://www.dropbox.com/scl/fi/0596ep5z4zk67nkch3uxf/Lecture-8-pinns-I.pptx?rlkey=lo7xh0ass7wf0wd9acn5jny73&st=xhxsomsw&dl=0)[Jupyter\_Notebook](Lecture_8_Notebook/Python_Codes)[MATLAB\_Codes](Lecture_8_Notebook/MATLAB_Codes)

**Lecture 9: Physics-Informed Neural Networks (PINNs)- Part II** [Slides: (April 7, 2025)](https://www.dropbox.com/scl/fi/wq128pvaytxts6s7ycg4c/Lecture-9-pinns-II.pptx?rlkey=0v8s1sjh0585udyggamvwtvxu&dl=0)

## Module III: Neural Operators
**Lecture 10: Deep Operator Network (DeepONet)** [Slides: (April 14, April 21, 2025)](https://www.dropbox.com/scl/fi/yfinwvwkaorgl3p5stmu9/Lecture_10_DeepONet_GK.pptx?rlkey=nvs1wwz8j53ea8rz61o3927zv&dl=0) [Jupyter\_Notebook](Lecture_10_Notebook/Python/operators.ipynb) [DATA\_FOR\_FNO](https://www.dropbox.com/s/klxu19gn9oxjdwf/burgers\_data\_R10.mat?dl=0)

**Lecture 11: Implementation of PINNs and DeepOnet** [Slides: (April 21, 2025)](https://www.dropbox.com/scl/fi/1o770q3ymfsmp2fl1jfcz/Lecture_11_implementation_PINNS_DeepXDE.pptx?rlkey=f0a0d3emzbpa9kthiz1kzzyvn&st=iym3tcwo&dl=0)[Jupyter\_Notebook](Lecture_11_Notebook/Python/deepXde.ipynb) [DATA\_FOR\_DEEPONET](https://www.dropbox.com/sh/dkmn84nccqcbuts/AAC9gunsRcCzfv4ETrTm56cWa?d
l=0)

## Module IV: SciML Uncertainty Quantification (SciML-UQ)

**Lecture 12: Machine Learning using Multi-Fidelity Data** [Slides: (April 21, April 27, 2025)](https://www.dropbox.com/scl/fi/kvkoqcabyn86079q0n0rv/Lecture_12_Multi-fidelity.pptx?rlkey=ibd7rd0ru7mjoldepe9urotlg&st=bldxidfv&dl=0) [Jupyter\_Notebook](Lecture_12_Notebook/multi_fidelity_notbook.ipynb)

**Lecture 13: Uncertainty Quantification(UQ) in Scientific Machine Learning** [Slides: (April 27, 2025)](https://www.dropbox.com/scl/fi/razs5yoe5svz7cirq2ik2/Lecture_13_UQ.pptx?rlkey=ywhygfnpt9z6h0z6z415cuuu9&dl=0) [Jupyter\_Notebook](Lecture_13_Notebook/neural_uq.ipynb) [Slides: Neural\_UQ](https://www.dropbox.com/scl/fi/w3x7lllewz7fppa8nx2mv/Lecture_13_ADD_ON_NeuralUQ.pptx?rlkey=j0an5lk1uuo3ftlxv3vmhdwc4&dl=0)

## Advanced Topics

1. **Multi-GPU Scientific Machine Learning** [Slides: (May 5, 2025)](https://www.dropbox.com/scl/fi/1tkn917z2a5r2h2jr9i28/Lecture_ADV_1_MULTI-GPU_SCIML.pptx?rlkey=21l7lz0zs0agpclk8lyqbe8nv&st=31ufkko2&dl=0) [Python Code](Advanced_Topics)

## Template for Project Presentation
[Example for Project Presntation](Example_Project_PPT/example_ppt_final_project.pdf)
[Project list](Project_list.pdf)

# Term Projects

1. **Biomedicine**
   * Solving forward and inverse problems in mathematical modeling of blood coagulation: [Project Files](https://www.dropbox.com/sh/n866zxh8cxdsqz1/AADBYT_5-xS8x94RDutOJ4Xza?dl=0)  
   * Predicting drug absorption using a physics-informed neural network: [Project Files](https://www.dropbox.com/sh/acdj0nb91zg4vzr/AADHQoabk7SrwM7aP5wuESywa?dl=0)
   * Parameter identification in Glucose-Insulin interaction: [Project Files](https://www.dropbox.com/sh/3dqxhlir7ij3k0p/AAAwzDKlUJQqb8BF5rePsmpwa?dl=0)
   * Parameter Estimation in Thrombus Formation: [Project Files](https://www.dropbox.com/sh/a5albb9toxl79cn/AAAxkUHoq1ZCin2KDKVEXDS2a?dl=0)

2. **Dynamical Systems**
   * Charged particle in a electromagnetic field: [Project Files](https://www.dropbox.com/sh/dktv3s13hu5lop4/AAAFgsb50_Ks0zxELoC3_7Hua?dl=0)
   * Learning dynamical systems from data: [Project Files](https://www.dropbox.com/sh/1ivo7t8uujh9zej/AADAEeF6SBeYQLt22cBF0ITXa?dl=0)

3. **Engine Dynamics**
   * Learning engine parameters: [Project Files](https://www.dropbox.com/sh/83xcrd7ossiog7r/AAAKHISuKugG91CB7OOVSsnxa?dl=0)

4. **Fluid Mechanics**
   * Compute and benchmark the solution of Boussinesq Equation using different activation functions: [Project Files](https://www.dropbox.com/sh/x0vcr25ylpi8jok/AACvAl3f4rV5Iv6rspES14TTa?dl=0)
   * Modeling Bubble Growth Dynamics: [Project Files](https://www.dropbox.com/sh/ep604br36ycsfih/AADbZ-5K4af-e1RRT2kEIRara?dl=0)
   * Reconstruction of flow past a cylinder: [Project Files](https://www.dropbox.com/sh/qoxsadqlo8yevmd/AACXkzaG5ToalNAYveVaoTqLa?dl=0)
   * Reconstruction of flow field for a lid driven cavity flow: [Project Files](https://www.dropbox.com/sh/if0auhruas9jnx9/AABEjNc6ynTCkjxJmHyDctR5a?dl=0)
   * Solving forward and inverse problems in mathematical modeling of wave propagation: [Project Files](https://www.dropbox.com/sh/j9yiutzgsafg9ie/AACCi1bQKQoDMM5iU2sli6I1a?dl=0)

5. **Geophysics**
   * Diffusion-Reaction in porous media: [Project Files](https://www.dropbox.com/sh/wmibretvmz49c33/AAAZfNsirVYUSHeVHESGV7UQa?dl=0)
   * Estimating sea-surface temperature using multi-fidelity data: [Project Files](https://www.dropbox.com/sh/2ny1m0jptxbw79s/AADy-rOr0RLJSRgKoRzEfkO4a?dl=0)
   * Microseismic hypocenter localization using PINNs: [Project Files](https://www.dropbox.com/sh/9jqvrx0hwu10ngq/AADkrBAWwu-usIjSxlCQsdpOa?dl=0)

6. **Heat Transfer**
   * Inverse heat transfer problem: [Project Files](https://www.dropbox.com/sh/63t4hl3ifu5hqwh/AAA_FpV7iDTNaLP8rXXPtAMRa?dl=0)
   * Steady state non-linear inverse heat conduction problem: [Project Files](https://www.dropbox.com/sh/mjkqntq6sdy0lzy/AAAWiG_xT4OMj5oIkOxVFPioa?dl=0)
   * Heat Conduction in Double Layered Structures exposed to Ultra-short Pulsed Laser: [Project Files](https://www.dropbox.com/sh/8h1v6tqm04hysrg/AAASSR5kpA4Kd6ft4imwVRcPa?dl=0)
   * Benchmarking Finite-difference vs Automatic-Differetiation for steady-state PDEs: [Project Files](https://www.dropbox.com/s/27etrkfjjbxvuy9/FDM_vs_AD.pdf?dl=0)

7. **Materials**
   * Inverse Problem on Modulus Identification of Hyperelastic Material: [Project Files](https://www.dropbox.com/sh/gzc7r9uokhf6qvp/AAAdcufJ9ktcJr-CYMWYPwUma?dl=0)
   * Characterizing surface breaking crack using ultrasound data and PINNs: [Project Files](https://www.dropbox.com/sh/rykynd704ulgng8/AABOHqZDwrILL7HvNhaC6mITa?dl=0)

APMA2070_S2025

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