Indian Institute of Technology Bombay

Machine Learning For Scientific Computing

Indian Institute of Technology Bombay

Civil Engineering

About Programme

Machine Learning (ML) is increasingly reshaping scientific computing by offering powerful alternatives for solving forward problems governed by ordinary and partial differential equations (ODEs/PDEs). Traditional numerical techniques, such as finite difference, finite element, and finite volume methods, often become computationally expensive for high-dimensional, nonlinear, or real-time applications. ML-based approaches—such as physics-informed neural networks (PINNs) and surrogate models—provide a data-driven paradigm for approximating solution operators, enabling rapid, scalable prediction of system responses under varying initial and boundary conditions. These methods can significantly accelerate simulations while maintaining consistency with underlying physical laws. For industry practitioners, this translates into faster design cycles, real-time digital twins, reduced reliance on expensive simulations, and the ability to perform large-scale parametric studies and optimization with minimal computational overhead. These tools are particularly relevant in sectors such as aerospace, energy, manufacturing, and infrastructure, where rapid decision-making and predictive insights are critical. This CEP workshop at IIT Bombay will introduce participants to key concepts, methodologies, and hands-on implementations of traditional numerical methods and ML techniques for forward solution of ODEs/PDEs. The integration of ML methods with classical numerical methods for efficient and reliable scientific computing will be explored, and a comparative study will be conducted against traditional methods. Hands-on training will be provided for the analysis of structural problems, post-processing and visualization using open source packages and cloud computing.

Programme Content

Topic details: (1) Numerical Methods: Fundamentals of numerical methods; Error analysis; Curve fitting; Solution of systems of linear equations; Numerical solution of differential equations. (2) Finite Element Method: Principles of discretisation; Element stiffness formulation based on direct, variational and weighted residual techniques and displacements, Numerical solution to ordinary/partial differential equations. (3) Machine Learning: Supervised Learning for regression; Linear Models and Generalized Linear Models (GLM) including Logistic Regression; Artificial Neural Networks (ANN); Physics-informed machine learning to solve ordinary/partial differential equations.

Programme Benefits

HANDS ON FACILITY:
The advanced computational laboratory in Civil Engineering will be used for hands-on training sessions. There will be two training sessions on i) Using the Python programming environment in Jupyter Notebook for analysis of ODE/PDE, post-processing and visualisation of the results, and ii) using Pytorch for building machine learning models and their application for solving ODE/PDE. Both sessions will use open-source platforms and free cloud storage for the training.

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Prashansa Uttam

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+91 9403890085[email protected]Mon – Fri, 9am – 5pm IST

Indian Institute of Technology Bombay

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https://www.iitb.ac.in
Mumbai, India

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Machine Learning For Scientific Computing | IIT Bombay