## Physics-informed Interpretable Machine Learning

### Midshipman Researcher(s): 2/C Wesley Nourachi

### Adviser(s): Professor Kevin McIlhany

### Poster #87

Traditional solutions to the diffusion equation are computationally expensive when boundary
conditions change with time. We have formulated an approximate matrix solution which is computationally
cheaper than traditional approaches and can be implemented in a neural network to find a higher-order
solution. Additionally, LiDAR point cloud data of urban infrastructure is one such case where
incredibly large datasets need to be reduced to much lower dimensionality while still maintaining
all the information contained therein. To that end, we have determined that neural networks are
capable of performing principle component analysis, although generally with less accuracy for
isolated structures.

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