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Hello Sir, |
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Hi @SachinJalan Thanks for reading through. Please have a look at https://www.geoelements.org/LearnMPM/point-axial-vibration1d.html#d-mpm-code-complete. Could you please write this in JAX? |
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Hello @kks32 , |
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Hi @SachinJalan That's great. Could we have a chat: https://calendly.com/krishnakut/30min book a time that's convenient for you. We can also find a different time if this does not work for you. |
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@kks32 HI sir, I am interested in this project and I went through the resources you provided , can I start working on it ? |
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Project Ideas
What is CB-Geo MPM
CB-Geo Material Point Method (MPM) is a large-deformation code for modeling particulate and fluid systems. MPM is a hybrid method that employs particles that traverse a background mesh to represent the physical state of the system.
Project 1: Differentiable Programming in MPM
Differentiable programming combines automatic differentiation with gradient based optimization that allows for solving inverse and design problems. Differentiable programming is a method of quickly solving complex numerical functions and combines two components: (1) automatic differentiation and (2) gradient-based optimization. In recent years, this method has gained popularity as a machine learning tool in the scientific community, with many applications including differentiable ray tracing algorithms or probabilistic programming.
Solving optimization and inverse problems are critical for engineering design and analysis. Despite the computational power, calculating derivatives, i.e., evaluating the forward simulation multiple times with small perturbations, is computationally very expensive and is prone to numerical instability. Traditional forward simulations cannot be used in machine learning models for optimization, as they cannot compute gradients with respect to the input parameters (reverse mode). This project involves developing a novel Differentiable Programming simulator that combines automatic reverse differentiation with a second-order gradient-based optimization algorithm, such as L-BFGS, to develop a fully-differentiable MPM simulator. Using the differentiable simulator, we can identify the input material properties by iteratively updating the input parameters by minimizing a loss function. Typically the loss function is the norm of the difference to the target observation. We then minimize this gradient (loss corresponding to the input parameters) using a second-order optimization algorithm. Differentiable MPM solves the exact PDE and can approximate the dynamics of its environment better than model-agnostic reinforcement learning methods. The differentiable MPM simulator will be written in Google JAX and exploits Tensor Processing Units to accelerate the computational time. We will demonstrate the functioning of the diff MPM code by extracting the input parameters for a collision of two deformable bodies. The differentiable MPM is a novel tool to provide gradients through a simulator, which can be coupled with existing machine learning algorithms to generate real-time decisions and optimization in robotics.
The main goals of this project are to:
Skills required:
Expected outcomes:
A prototype that offers the features of differentiable programming to MPM to solve inverse, optimization, and design problems. We'll solve for input parameters given an output result variable using different optimization routines like ADAM and SGD.
Skills required:
Benefits of working on this project
Students who work on this project can expect their skill-set to grow in
Benefits to project/community
Helpful Experience
First steps
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