Artificial Neural Networks : Solving ODEs and PDEs

Python Code for solving ODEs using ANNs:
towardsdatascience.com/how-to...
Physics Inspired Neural Networks:
www.sciencedirect.com/science...
Artificial Neural Networks : A Simple Introduction
• Artificial Neural Netw...
Backpropagation algorithm:
• Artificial Neural Netw... ​
#DataScience​​​​ #MachineLearning​​​​ #ArtificialNeuralNetwork​ #ANN​ #DeepLearning​ #ReLU​ #Sigmoid​ #Activation​ #ActivationFunction​ #UniversalApproximationTheorem​ #LogisticRegression​ #Probability​​​​ #SupervisedLearning​​​ #ODE #PDE

[@sanaullahsaqib2168]

Why we use ANNs on ODEs.
What is difference to get Solution from numerical methode and also get the solution from the ANNs. Why we use ANNs ?

[@ShirshakkPurkayastha]

Does the Curse of Dimensionality have any role in restricting the ANN model performance while solving ODEs and PDEs?

[@EvolutionaryIntelligence]

That depends on the range of values over which you are trying to solve the ODE/PDE. If the ODE/PDE is well behaved, an analysis over a short range of parameter values is sufficient, in which case the dimensionality should not be a problem.

[@AyushMathur-tu2ms]

Are there specific ODE forms which cannot be solved practically using the available techniques or computational limitations in ANN, although the universal approximation theorem may be valid?? Is the curse of dimensionality an issue here?

[@EvolutionaryIntelligence]

Thats a good question but hard to answer since very limited work has been done on applying ANN for solving ODEs.

[@Kishan31468]

Neural network for solving ODE is at very nascent stage. There is a lot to do. Numerical methods serve very well as of now. We don't need neural network for that. Can I have your linkedin ID.

[@AnirudhKalla]

Why don't we minimize the DE and Boundary Conditions separately. In this combined case, we cant actually see which of the two is getting minimized less/more, right?

[@EvolutionaryIntelligence]

How do you minimise them separately? Finally you need a single cost function to be minimised. You can always compute the two terms separately after each forward pass to decide the stopping criterion.

[@SwadhinAgrawal-ix7xi]

There can be ODE's with more than one solution, so do we need to train the network that many times? or one training is sufficient?

[@SwadhinAgrawal-ix7xi]

I think we are training for only a particular solution, so we can't really say that we have solved an ODE

[@EvolutionaryIntelligence]

Yes, with ANN, we are not finding a symbolic solution for the ODE. So we have to specify the initial conditions and we will get the corresponding solution.

[@aishaummer5817]

simply what does it mean by training a network???plss answer...

[@EvolutionaryIntelligence]

Watch this video on the Backpropagation algorithm : ua-cam.com/video/ntnwjWEpnkk/v-deo.html