Channel Title: elastropy Channel Description: Learn beginner to advanced-level skills from experts, at your own pace and on your own schedule. Our trainings dive deep into two key areas: 1 - Machine Learning: Get a solid foundation in theory and learn to use Python libraries like Scikit-learn, PyTorch, and TensorFlow etc to program your ML models from scratch. 2 - Finite Element Analysis (FEA) - Linear and Nonlinear: Get a solid foundation in theory and learn to program your own FEA programs from scratch in Python. We also cover practical applications using tools like OpenSees, OpenSeesPy, LS-Dyna, ANSYS, COMSOL and Abaqus. So, if you're keen on mastering these skills, you're in the right place! Join our telegram group for more updates - https://telegram.me/elastropy_official (if the above link does not work, then search for (without quotes) "elastropy", you will find a group named elastropy.com ) <video> DeepXDE Tutorial #5: Mastering the Error() Method – Residuals & Gradients in PINNs Description: Video-ID-V54 In this tutorial, we dive deep into the powerful `error()` method in DeepXDE, an essential feature for working with Physics Informed Neural Networks (PINNs). Learn how to evaluate residuals and enforce boundary conditions, including Dirichlet, Neumann, Robin, Periodic, and Operator BCs. We also compare the use of model.predict() and model.net(), highlighting their differences, advantages, and when to use each effectively. Whether you're new to PINNs or looking to sharpen your skills, this tutorial is packed with practical insights. 💡 What You'll Learn: - What is the `error()` method, and why is it essential for PINNs? - How to handle various boundary conditions in DeepXDE. - Key differences between model.predict() and model.net(). - Practical demonstrations for Dirichlet, Neumann, Robin, and Operator BCs. If you have any questions, drop them in the comments, and don’t forget to like, share, and subscribe for more tutorials like this. Happy learning! 🎓 </video> <video> Physics Informed Neural Networks (PINNs): Solving the Burgers Equation Step-by-Step Tutorial Description: Video ID - V49 Learn how to solve the Burgers' equation using Physics Informed Neural Networks (PINNs) in this step-by-step tutorial! This video is perfect for anyone interested in machine learning, neural networks, or partial differential equations (PDEs). We'll start by explaining what PINNs are and how they differ from traditional machine learning models. You’ll learn how to leverage physical laws to train a neural network, even with limited data. The focus is on solving the nonlinear 1D Burgers' equation using PyTorch. What you'll learn: - Introduction to Physics-Informed Neural Networks (PINNs). - Detailed implementation of the Burgers' equation using PINNs. - Defining loss functions for initial conditions, boundary conditions, and PDE residuals. - Training a simple feedforward neural network in PyTorch with step-by-step code. - Evaluating model performance using collocation points and contour plots. This tutorial covers everything from formulating the loss function to evaluating results. The Burgers' equation is often used as a benchmark in numerical analysis and machine learning research, making this tutorial a great resource for researchers and students. If you find this video helpful, please like, comment, and subscribe for more tutorials on machine learning and neural networks. Your support helps us create more educational content! </video> <video> DeepXDE Tutorial #7: Master Solving System of ODEs with PINNs Using DeepXDE Description: Video-ID-V56 Welcome to our DeepXDE tutorial series! In this video, we explore how to solve a system of coupled ordinary differential equations (ODEs) using Physics-Informed Neural Networks (PINNs) with the DeepXDE library. This step-by-step guide includes everything from defining the ODE system, setting up initial conditions, and training a neural network to visualizing the results and validating the accuracy. What you'll learn in this video: - Learn how to use DeepXDE for solving ODEs with PINNs. - Understand how to encode ODE systems, define initial conditions, and validate solutions. - Gain insights into evaluating model performance with metrics and visualization. Timestamps: 00:00 Introduction – Overview of the tutorial and key learning objectives 01:49 Are you new to this tutorial series?? 02:18 Overview of the ODE system and Exploring Reference Solution 03:53 Setting up the System of ODE residuals, ICs and analytical solution functions 08:12 Domain setup, dataset preparation, Neural Network Configuration and Training 12:36 L2 Relative Error - Verify the differences 14:48 Visualizing results: PINN vs Analytical Solutions 15:36 Comment your questions Make sure to watch the previous tutorials in the series for a complete understanding of DeepXDE. Playlist link: https://www.youtube.com/playlist?list=PLM7DTyYjZGuLYDLV9g7AqkEatySe-lAqG Tutorial Series tentative curriculum: https://elastropy.notion.site/Exploring-the-Potential-of-DeepXDE-A-Tentative-Curriculum-for-the-Ultimate-Tutorial-Series-13f8b834612a80aa8b07cf6a24b9796d If you find this tutorial helpful, please like the video and subscribe to our channel for more in-depth tutorials like this. Feel free to leave your questions or suggestions in the comments below! Happy Learning! 🎓 </video> <video> Physics Informed Neural Networks (PINNs) for Solving System of ODEs - A Beginner's Tutorial Description: Video ID - V48 Welcome to another exciting tutorial on Physics-Informed Neural Networks (PINNs). In this video, we explore how PINNs can be used to solve ordinary differential equations (ODEs). You'll gain a complete understanding of both the theory behind PINNs and the practical steps to implement them. We'll cover: - An introduction to PINNs and how they incorporate physics into the learning process. - A step-by-step guide to using neural networks to solve ODEs. - Setting up the neural network architecture, formulating the loss function, and understanding collocation points. - Training the network using popular optimizers like Adam and lbfgs. Throughout this tutorial, we solve a system of ODEs and compare the neural network solution with traditional analytical methods. If you're new to PINNs or want to expand your understanding, this video will help you get started. If you find this content valuable, please support us by subscribing and liking the video. Your support motivates us to keep producing more in-depth tutorials. Stay tuned for upcoming videos where we will tackle advanced topics like solving partial differential equations, inverse problems, and much more using PINNs. Don't forget to subscribe so you don’t miss any of our content. Let’s aim for 500 likes on this video – thank you for your amazing support! </video> <video> DeepXDE Tutorial #1: DeepXDE Setup and Overview | Physics Informed Neural Networks Description: Video ID - V50 In this comprehensive tutorial, we explore DeepXDE, a Python library for solving a wide variety of differential equations using deep learning with Physics Informed Neural Networks. This video walks you through the process of solving a 1D Poisson equation, from defining the governing differential equation to applying boundary conditions and training a neural network. Key topics covered include: - DeepXDE Setup and Overview - Introduction to the DeepXDE library for solving differential equations. - Setting up the geometry and boundary conditions (Dirichlet conditions) for a 1D domain. - Generating collocation points and preparing training data. - Training a neural network to solve the equation using DeepXDE. - Visualizing the solution with Matplotlib and comparing it to the true solution. - Exploring advanced features like generating animations to visualize training progress. Stay tuned for the next tutorial, where we’ll cover more fundamental topics such as defining governing differential equations, boundary conditions, Hessian, Jacobian etc. Perfect for anyone interested in using machine learning to solve differential equations! </video> <video> Automated Machine Learning Using TPOT- Concrete Strength Prediction Using Machine Learning Libraries Description: Video ID - V44 Discover how to automate concrete strength prediction using TPOT, a powerful tool for Automated Machine Learning (AutoML), in Python. In this video, we guide you through the process of setting up TPOT, preparing your data, and leveraging its optimization capabilities to find the best machine learning pipeline. You’ll learn how to configure and run TPOT to automatically explore and optimize various machine learning models, making the model selection process efficient and straightforward. Using TPOT, you can take advantage of automation to streamline your machine learning workflow, making it easier to discover the most effective models without the extensive manual trial and error typically involved. This makes the process accessible and efficient, ideal for data scientists and engineers looking to apply AutoML to materials science applications. #machinelearning #automl #GradientBoosting #sklearn #civilengineering #concretestructures #regressionanalysis </video> <video> DeepXDE Tutorial #2: Setting Up ODEs/PDEs & Boundary Conditions with Jacobian and Hessian Description: Video-ID-V51 In this tutorial, we explore Physics Informed Neural Networks (PINNs) using DeepXDE, a specialized tool for solving differential equations with Neural Networks. Learn to set up a governing differential equation through a 1D Poisson equation example and implement Dirichlet and Neumann boundary conditions. We also introduce the Jacobian and Hessian functions, crucial for evaluating first and second-order derivatives within PINNs. This video is perfect for those starting with DeepXDE or seeking to enhance their understanding of PINNs in differential equation modelling. </video> <video> Physics Informed Neural Networks (PINNs) || Ordinary Differential Equations || Step-by-Step Tutorial Description: Video ID - V46 In this tutorial, we'll explore how to solve the 1D Poisson equation using Physics Informed Neural Networks (PINNs). You'll learn about the fundamentals of the Poisson equation, the integration of physical laws into neural networks, and how to set up, build, and train a PINN to solve this important equation. Follow along with our hands-on coding examples and gain practical insights into applying PINNs for solving differential equations. Perfect for both beginners and advanced learners, this video provides a comprehensive yet straightforward approach to mastering PINNs. Physics Informed Neural Networks PINNs, Rethinking Physics Informed Neural Networks, Physics Informed Machine Learning- High Level Overview of AI and ML in Science and Engineering, Introduction to Physics Informed Neural Networks - A hands on, project based course, Physics Informed Neural Networks PINNs - An Introduction, Learning Physics Informed Machine Learning, How Do Physics-Informed Neural Networks Work?, Physics-informed neural networks for fluid mechanics, Get hands On with PINNs, Physics Informed Neural Networks - an intuitive explanation - Introduction, Physics Informed Neural Networks PINNs for approximating PDEs, Physics Informed Neural Network PINNs: Step by Step plan, Inverse Physics Informed Neural Networks I-PINNs, Physics-informed neural networks for fluid mechanics, Neural Network to Solve Navier-Stokes Equations. Subscribe to our channel for more exciting machine learning tutorials. Join us on this journey to unlock the potential of machine learning in civil engineering applications. </video> <video> DeepXDE Tutorial #6: Master Solving Burgers Equation with PINNs Using DeepXDE Description: Video-ID-V55 In this comprehensive tutorial, we dive into solving Burgers equation using Physics Informed Neural Networks (PINNs) with the DeepXDE library. This session is part of our ongoing series on leveraging DeepXDE for solving differential equations. Whether you're a beginner or an advanced user, this tutorial will guide you through every step of the process, from setting up the problem to evaluating the results. What you'll learn in this video: - Understanding evaluation of partial derivatives using Jacobian and Hessian functions. - Applying boundary and initial conditions. - Creating a combined space-time geometry domain. - Evaluating test metric using external function. - Training a PINN model to solve Burgers equation. - Visualizing results with contour and line plots. Timestamps: 0:00 Introduction – Overview of the tutorial and key learning objectives 2:10 Burgers' Equation Definition, Importing Libraries and Exploring Reference Solution 5:12 Computing Partial Derivatives For Scalar and Vector Valued Functions Using Jacobian and Hessian 19:20 Defining Initial and Boundary Conditions 22:16 Defining Combined Space-Time Geometry Domain 23:31 Model Setup and Neural Network Design 25:56 Test Metric Evaluation Using External Function and Training and Verifying Test-Metric 29:59 Result Visualization – Contour plots and line plots for analysis 32:15 Conclusion and Next Steps – Tips for improving accuracy and preview of future tutorials Previous Tutorials in the Series: https://www.youtube.com/playlist?list=PLM7DTyYjZGuLYDLV9g7AqkEatySe-lAqG Tutorial Series tentative curriculum: https://elastropy.notion.site/Exploring-the-Potential-of-DeepXDE-A-Tentative-Curriculum-for-the-Ultimate-Tutorial-Series-13f8b834612a80aa8b07cf6a24b9796d If you find this tutorial helpful, please like the video and subscribe to our channel for more in-depth tutorials like this. Feel free to leave your questions or suggestions in the comments below! Happy Learning! 🎓 </video> <video> DeepXDE Tutorial #8: Mastering Callbacks to Automate & Visualize Neural Network Training Predictions Description: Video-ID-V57 Welcome to our DeepXDE tutorial series! In this video tutorial, we dive deep into mastering callbacks in the DeepXDE library and showcase how to implement them effectively to automate and visualize your neural network training process. Using a fourth-order Euler beam problem as an example, we demonstrate how to set up callbacks to save predictions during training and use them to create animations that visualize the model’s training progress. This tutorial is your complete guide to understanding callbacks in DeepXDE. What you'll learn in this video: - Learn the fundamentals of callbacks in DeepXDE. - Understand how to automate saving epoch level predictions during training. - Explore how to use saved epoch level predictions to generate animations visualizing model improvement. - Gain insights into combining multiple callbacks for enhanced training control. Timestamps: 00:00 Introduction – Overview of the tutorial and learning objectives 02:31 What Are Callbacks? – Understanding their purpose and use cases 04:00 Euler Beam Problem – Defining prerequisites and Neural Network configuration 07:19 Callbacks – Dive deep 14:11 Generating Animations – Visualizing predictions over training epochs 17:58 Additional callbacks examples and combining multiple custom callback functions 19:19 Closing remarks Make sure to watch the previous tutorials in the series for a complete understanding of DeepXDE. Playlist link: https://www.youtube.com/playlist?list=PLM7DTyYjZGuLYDLV9g7AqkEatySe-lAqG Tutorial Series tentative curriculum: https://elastropy.notion.site/Exploring-the-Potential-of-DeepXDE-A-Tentative-Curriculum-for-the-Ultimate-Tutorial-Series-13f8b834612a80aa8b07cf6a24b9796d If you find this tutorial helpful, please like the video and subscribe to our channel for more in-depth tutorials like this. Feel free to leave your questions or suggestions in the comments below! Happy Learning! 🎓 </video> <video> Regression Using a Linear GAM - Concrete Strength Prediction Using Machine Learning Libraries Description: Video ID - V45 Explore how to predict concrete strength using regression with a Linear Generalized Additive Model (GAM) in Python. In this video, we demonstrate the process step-by-step using popular machine learning libraries. Learn how to preprocess data, build the GAM model, and evaluate its performance. Perfect for data scientists and engineers looking to apply machine learning to materials science! #machinelearning #GradientBoosting #sklearn #civilengineering #concretestructures #regressionanalysis </video> <video> DeepXDE Tutorial #3: Robin and Periodic Boundary Conditions Description: Video-ID-V52 In this tutorial, we dive into advanced boundary conditions for Physics Informed Neural Networks (PINNs) using DeepXDE. We'll explore how to implement *Robin* and *Periodic boundary conditions* , two critical types that can significantly impact the accuracy and stability of your neural network solution. We’ll discuss the unique challenges these boundary conditions present, particularly for network convergence, and demonstrate the code setup step-by-step. *Topics Covered:* - What are Robin and Periodic Boundary Conditions? - Step-by-step implementation in DeepXDE - Introduction to custom BCs, soft and hard boundary constraints Don't forget to like, subscribe, and hit the bell icon to stay updated with more tutorials on advanced PINN techniques! </video> <video> DeepXDE Tutorial #4: Solving the Euler Beam Equation with Custom Boundary Conditions Description: Video-ID-V53 Dive into the world of Physics Informed Neural Networks (PINNs) with this comprehensive tutorial! In this third video of our boundary conditions series, we explore how to define and apply custom boundary conditions using the OperatorBC command in DeepXDE. Using the Euler Beam Equation as our example, we demonstrate how to solve complex fourth-order differential equations with higher-order and mixed boundary conditions, providing step-by-step guidance. 📚 Key Topics Covered: - Understanding custom and non-standard boundary conditions - Defining second- and third-order derivative boundary conditions - Implementing custom BCs using OperatorBC in DeepXDE - Solving the Euler Beam Equation with Dirichlet, Neumann, and OperatorBCs - Comparing PINN solutions with analytical solutions for accuracy 🎓 Whether you're new to PINNs or looking to enhance your skills, this video is packed with insights and practical examples to help you get started. Don't miss the next tutorial, where we'll explore residual errors for various boundary conditions! 🔔 Subscribe to our channel for more hands-on tutorials and deep dives into PINNs, DeepXDE, and advanced computational techniques. #DeepXDE #EulerBeamEquation #PhysicsInformedNeuralNetworks </video> <video> DeepXDE Tutorial #9: Solving Nonlinear System of PDEs: Schrödinger Equation with PINNs || PyTorch Description: Video-ID-V58 Welcome to our DeepXDE tutorial series! In this video tutorial, we take a deep dive into solving the Nonlinear Schrödinger Equation using Physics Informed Neural Networks (PINNs) in DeepXDE. This equation, a complex-valued Nonlinear System of PDEs, presents unique challenges and opportunities for applying PINNs effectively. We'll explore how to break the problem into real and imaginary components, set up boundary and initial conditions, and validate solutions through advanced techniques like residual checks and energy conservation. Using a structured approach, this tutorial provides a complete guide to understanding and solving nonlinear PDE systems with DeepXDE. ### What you'll learn in this video: - Understand the nonlinear Schrödinger equation as a Nonlinear System of PDEs. - Learn how to configure PINNs for solving complex-valued equations in DeepXDE. - Master techniques for validating PINN solutions using residuals, boundary conditions, and intrinsic physical properties like energy conservation. - Explore solution visualization and comparison with reference solutions. ### Timestamps: 00:00 - Happy New Year!!! 00:23 - Thank You For Your Support 00:43 - Introduction – Overview of the tutorial and key learning objectives 03:10 - Understanding NLSE as a Nonlinear System of PDEs 05:03 - Breaking NLSE, BCs and ICs into Real & Imaginary Components 08:18 - Configuring the Neural Network for Nonlinear System of Equations 18:46 - Training & Model Refinement using L-BFGS Optimizer 21:32 - Postprocessing and Visualization of Results 23:13 - Validating PINN Solutions Without Reference Data 31:03 - Second Level Accuracy Validation 35:38 - Comparing Solutions with Reference Data 37:18 - Evaluating Solutions any Single Point 38:23 - Closing Remarks & Final Thoughts Make sure to watch the previous tutorials in the series for a complete understanding of DeepXDE. *Playlist link:* https://www.youtube.com/playlist?list=PLM7DTyYjZGuLYDLV9g7AqkEatySe-lAqG *Tutorial Series Tentative Curriculum:* https://elastropy.notion.site/Exploring-the-Potential-of-DeepXDE-A-Tentative-Curriculum-for-the-Ultimate-Tutorial-Series-13f8b834612a80aa8b07cf6a24b9796d If you find this tutorial helpful, please like the video and subscribe to our channel for more in-depth tutorials like this. Feel free to leave your questions or suggestions in the comments below! *Happy Learning! 🎓* </video> <video> Solving Newton's Law of Cooling with Physics Informed Neural Networks (PINNs) Description: Video ID - V47 In this video, we explore the power of Physics-Informed Neural Networks (PINNs) to solve Newton's Law of Cooling, a fundamental differential equation in physics. We begin by introducing the theoretical background of Newton’s law and how PINNs combine machine learning with physical principles to model complex systems. You will gain a detailed understanding of how to build and train a neural network using Python and TensorFlow to simulate temperature evolution over time. Throughout this tutorial, we cover: - An overview of Newton's Law of Cooling - The role of neural networks in solving differential equations - Building a feed-forward neural network with TensorFlow - Training the PINN model to match the analytical solution - Using collocation points and multi-weight loss functions to improve model accuracy - Fine-tuning the model and understanding the impact of changing parameters By the end of the video, you will have a strong foundation in using PINNs to solve differential equations like Newton's Law of Cooling, and you'll be equipped to tackle more complex scenarios in scientific machine learning. If you enjoyed the video, don't forget to like, subscribe, and hit the bell icon to stay updated with more tutorials on deep learning and physics-informed models. Feel free to leave questions or suggestions in the comments below, or contact us via email. Happy learning! </video>

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Description

Learn beginner to advanced-level skills from experts, at your own pace and on your own schedule. Our trainings dive deep into two key areas:

1 - Machine Learning: Get a solid foundation in theory and learn to use Python libraries like Scikit-learn, PyTorch, and TensorFlow etc to program your ML models from scratch.

2 - Finite Element Analysis (FEA) - Linear and Nonlinear: Get a solid foundation in theory and learn to program your own FEA programs from scratch in Python. We also cover practical applications using tools like OpenSees, OpenSeesPy, LS-Dyna, ANSYS, COMSOL and Abaqus.

So, if you're keen on mastering these skills, you're in the right place!

Join our telegram group for more updates - https://telegram.me/elastropy_official
(if the above link does not work, then search for (without quotes) "elastropy", you will find a group named elastropy.com )

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