Neural Oscillators for Generalization of Physics-Informed Machine Learning
Authors: Taniya Kapoor, Abhishek Chandra, Daniel M. Tartakovsky, Hongrui Wang, Alfredo Nunez, Rolf Dollevoet
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Numerical Experiments |
| Researcher Affiliation | Academia | 1Department of Engineering Structures, Delft University of Technology, The Netherlands 2Department of Electrical Engineering, Eindhoven University of Technology, The Netherlands 3Department of Energy Science and Engineering, Stanford University, USA |
| Pseudocode | No | The paper contains mathematical equations describing the model, but no structured pseudocode or algorithm blocks were found. |
| Open Source Code | Yes | The codes to reproduce the presented results are provided at https://github.com/taniyakapoor/AAAI24 Generalization |
| Open Datasets | Yes | The four equations viscous Burgers equation, Allen-Cahn (AC) equation, nonlinear Schr odinger equation (NLS) and Euler-Bernoulli beam equation along with their boundary and initial conditions are provided in the supplementary material SM B. The reference for the Euler-Bernoulli beam equation is an analytical solution described in SM B. |
| Dataset Splits | No | While the paper mentions "until its validation error stabilizes" in the context of PINN training, it does not provide specific details on the dataset split for validation (e.g., percentages, sample counts, or how it is distinct from the training data). |
| Hardware Specification | Yes | The software and hardware environments used to perform the experiments are as follows: UBUNTU 20.04.6 LTS, PYTHON 3.9.7, NUMPY 1.20.3, SCIPY 1.7.1, MATPLOTLIB 3.4.3, TENSORFLOW-GPU 2.9.1, PYTORCH 1.12.1, CUDA 11.7, and NVIDIA Driver 515.105.01, i7 CPU, and NVIDIA GEFORCE RTX 3080. |
| Software Dependencies | Yes | The software and hardware environments used to perform the experiments are as follows: UBUNTU 20.04.6 LTS, PYTHON 3.9.7, NUMPY 1.20.3, SCIPY 1.7.1, MATPLOTLIB 3.4.3, TENSORFLOW-GPU 2.9.1, PYTORCH 1.12.1, CUDA 11.7, and NVIDIA Driver 515.105.01, i7 CPU, and NVIDIA GEFORCE RTX 3080. |
| Experiment Setup | Yes | To predict a solution to Burgers equation in X1 using PINNs, 1600 training points are used, comprising 1000 residual points and 600 points for boundary and initial time. The feedforward neural network has two inputs, space x D and time t T. Four hidden layers, each containing 20 neurons, and hyperbolic tangent (tanh) activation function are used to predict the approximation of the solution u U. Optimization is performed using the LBFGS algorithm for 3500 epochs. ... The input and output size of the recurrent networks is taken to be kx, with a single hidden layer of size 32. The sequence length is chosen to be kt. ... ADAM optimizer is used to train the recurrent networks. The learning rates for LEM, Co RNN, GRU, LSTM, and RNN are 0.001, 0.001, 0.01, 0.01, and 0.01, respectively, across all equations. For Schr odinger equation, a learning rate of 0.01 is used to train the LEM. In the case of Co RNN, two additional hyperparameters, γ and ϵ, are set to 1.0 and 0.01, respectively. The number of epochs executed for Burgers and Allen Cahn equations is 20, 000, while for Schr odinger equation, it is 30, 000. Lastly, 200, 000 epochs are performed for the Euler-Bernoulli beam equation. |