Thank you so much for sharing this interesting project. Just had a question that if we use 'ReLU' activation function for the first layer in our Neural Network, then the ouput of each node from the first layer would be non-negative. Would adding constraints for the parameters of the first layer in this case also help to improve the performance of the model?
That's an interesting observation and likely another way to enforce a positive output constraint. Many of the machine learning packages also allow constraints to be specified now: www.tensorflow.org/api_docs/python/tf/keras/constraints
Thanks for the demonstration. What was the reason of leaving W2 parameters without the constraint of >=0? Would it be non-physical to set the constraint on W2?
It would be interesting to try different combinations of constraints on the layers. The idea with the constraint on the first layer is that it relates to group contribution methods where each additional group needs to have a positive effect on the outcome (e.g. Parachor value). Here is additional information on the approach: ua-cam.com/video/a5JNGujVbnw/v-deo.html and a publication: Babaei, M.R., Stone, R., Knotts, T.A., Hedengren, J.D., Physics-Informed Neural Networks with Group Contribution Methods, Journal of Chemical Theory and Computation, American Chemical Society, 2023, DOI: 10.1021/acs.jctc.3c00195.
That is an interesting topic. Symbolic solutions are typically only applicable to small scale systems but produce exact results. Numerical methods are better when there is more data and with more complex models. Here is some material on both methods: apmonitor.com/pds/notebooks/10_solve_equations.html
PINN is possible when you have constraints or structure of the neural network that is guided by physics equations. If you have both data and physics-information then it should be possible.
Hello Doctor...I am working on solving the problem of trajectory planning for humanoid robots that are similar to humans..Actually, trajectory planning for these robots is very difficult and complicated because of the large number of degrees of freedom that makes the number of paths set to move the robot from a primitive position to a target position. Infinite..and to solve this problem, I will design an estimate capable of predicting human behavior..input to the required task and output for angular variables..but to design this estimator I have to model the human body...central nervous system, muscles, bones, etc.. The central nervous system is often represented using dynamic optimization theory. The question I want to ask is what kind of processor and numerical methods I should choose to be able to solve these complexities in real time.
![Rethinking Physics Informed Neural Networks [NeurIPS'21]](/img/n.gif)
Thanks for sharing professor, it will be cool to apply it using the tinyML framework
Thank you so much for sharing this interesting project. Just had a question that if we use 'ReLU' activation function for the first layer in our Neural Network, then the ouput of each node from the first layer would be non-negative. Would adding constraints for the parameters of the first layer in this case also help to improve the performance of the model?
That's an interesting observation and likely another way to enforce a positive output constraint. Many of the machine learning packages also allow constraints to be specified now: www.tensorflow.org/api_docs/python/tf/keras/constraints
Thanks for the demonstration. What was the reason of leaving W2 parameters without the constraint of >=0? Would it be non-physical to set the constraint on W2?
It would be interesting to try different combinations of constraints on the layers. The idea with the constraint on the first layer is that it relates to group contribution methods where each additional group needs to have a positive effect on the outcome (e.g. Parachor value). Here is additional information on the approach: ua-cam.com/video/a5JNGujVbnw/v-deo.html and a publication: Babaei, M.R., Stone, R., Knotts, T.A., Hedengren, J.D., Physics-Informed Neural Networks with Group Contribution Methods, Journal of Chemical Theory and Computation, American Chemical Society, 2023, DOI: 10.1021/acs.jctc.3c00195.
What is your opinion on symbolic regression in this context? There you could explicitly add analytically proven priors and constraints.
That is an interesting topic. Symbolic solutions are typically only applicable to small scale systems but produce exact results. Numerical methods are better when there is more data and with more complex models. Here is some material on both methods: apmonitor.com/pds/notebooks/10_solve_equations.html
Blending the two methods would be an interesting area of research.
Thank you for sharing.
amazing work! thank you!
Hello professor, can we use PINN for prediction travel time?
PINN is possible when you have constraints or structure of the neural network that is guided by physics equations. If you have both data and physics-information then it should be possible.
Hello Doctor...I am working on solving the problem of trajectory planning for humanoid robots that are similar to humans..Actually, trajectory planning for these robots is very difficult and complicated because of the large number of degrees of freedom that makes the number of paths set to move the robot from a primitive position to a target position. Infinite..and to solve this problem, I will design an estimate capable of predicting human behavior..input to the required task and output for angular variables..but to design this estimator I have to model the human body...central nervous system, muscles, bones, etc.. The central nervous system is often represented using dynamic optimization theory. The question I want to ask is what kind of processor and numerical methods I should choose to be able to solve these complexities in real time.
This course may help: apmonitor.com/do
Hi professors, how can I get his notebook ?
The source files are available at apmonitor.com/pds/index.php/Main/ThermophysicalProperties
Hello