Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem
Abstract
:1. Introduction
2. PINN Architecture
3. A First Order ODE Example
4. A PINN for the Classical Reynolds Equation
5. Concluding Remarks
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Value |
---|---|---|
# of grid points for the solution domain | 41 | |
# of training batches (# or corrections during 1 Epoch) | 1000 | |
# of Epochs (1 Epoch contains training batches) | 100 | |
Learning rate coefficient (relaxation for the update) | 0.01 | |
N | # of nodes/neurons in the hidden layer | 10 |
Node | ||||
---|---|---|---|---|
1 | 1.8500 | −0.5946 | −3.5805 | 0.3055 |
2 | 1.8588 | 1.5974 | 0.9712 | |
3 | 0.3025 | 1.9241 | 0.8921 | |
4 | 1.4546 | 0.3742 | −0.9955 | |
5 | 0.5065 | 1.2535 | −0.1430 | |
6 | −1.0898 | −1.0199 | −1.1067 | |
7 | −0.8302 | 0.3519 | −1.1668 | |
8 | 0.3789 | 1.6502 | 0.1754 | |
9 | 2.5012 | 0.7657 | 1.2955 | |
10 | 2.2743 | 1.4172 | 1.2787 |
Parameter | Description | Value |
---|---|---|
# of grid points for the solution domain | 21 | |
K | Slope parameter for the Reynolds equation | 1 |
# of training batches (# or corrections during 1 epoch) | 2000 | |
# of Epochs (1 epoch contains training batches) | 600 | |
Learning rate coefficient (relaxation for the update) | 0.005 | |
N | # of nodes/neurons in the hidden layer | 10 |
Node | ||||
---|---|---|---|---|
1 | 0.0557 | 1.9808 | −0.2186 | −0.0641 |
2 | −6.3047 | 6.1664 | 0.1220 | |
3 | −9.3674 | 11.4571 | 0.3843 | |
4 | −4.5473 | 3.3266 | 0.0305 | |
5 | −2.4464 | −1.9884 | 0.1188 | |
6 | −0.1365 | −0.1674 | 0.4155 | |
7 | 0.8581 | 0.5253 | 0.5089 | |
8 | 1.0901 | 2.0858 | 0.3348 | |
9 | 0.2085 | 0.2523 | −0.2024 | |
10 | −3.2168 | 5.9722 | −0.9899 |
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Almqvist, A. Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem. Lubricants 2021, 9, 82. https://doi.org/10.3390/lubricants9080082
Almqvist A. Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem. Lubricants. 2021; 9(8):82. https://doi.org/10.3390/lubricants9080082
Chicago/Turabian StyleAlmqvist, Andreas. 2021. "Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem" Lubricants 9, no. 8: 82. https://doi.org/10.3390/lubricants9080082
APA StyleAlmqvist, A. (2021). Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem. Lubricants, 9(8), 82. https://doi.org/10.3390/lubricants9080082