Here we are currently working to generate a machine learning model to generate the solution of Differential equations.
This is an exploratory project done by students PRANAV S, NOORSHABA, ADITHYA, PRIYANKA SONY of Second year Mathematics and Computing (IDD) IIT BHU under the supervision of Prof V.K.Singh faculty-Dept of Mathematical science IIT BHU and Mr Abhishek Kumar Singh, Research scholar IIT Delhi.
In this project in the initial stage we learnt the basic princles of machine learning and various ML algorithms useful in Applied mathematics. Later we analysed several research papers mainly focused on the research regarding the optimised methods to find solutions of partial differential equations. We deeply explored the possibilites of Sparcial optimization, L1 norms, LASSO (Least Absolute Shrinkage and Selection Operator), Automatic differencian, Application of Gaussian process, Spatio Temporal datasets and lot more.
On the basis of the inferences drawn from the research papers we are currently working to create an ML model to effictively predict the solution of differential equations. Currently on the first phase of the project we have reviewed the research papers "Deep Hidden Physics Models: Deep learning of non linear Partial Differential Equations" by Maziar Raissi and "Partial differential equation via data discovery and sparse optimisation" by Hayden Schaeffer.
The inferences drawn from several research papers that we went through are given in the ppts uploaded in the repository.
You can read the final report of the first phase of the projecrt here : https://github.com/Dark-knight-02/Solution-of-Differential-Equations-using-Machine-Learning/blob/main/Exploratory%20Project%20Report.pdf
And the final presentation : https://github.com/Dark-knight-02/Solution-of-Differential-Equations-using-Machine-Learning/blob/c61309c434480b3b1628dbc0d201790682128e8f/Exploratory%20Project%20Final%20Presentation.pptx