Colin G. Cess, Stacey D. Finley

Read the preprintIn our recent preprint entitled “Siamese neural networks for a generalized, quantitative comparison of complex model outputs”, we developed an approach to holistically compare model simulations without the need to specify a comparison metric. This method accounts for how model outputs are related, including relationships that would be impossible to manually calculate. We do this by using Siamese neural networks

**Figure 1**: Overview of using a Siamese neural network to project a pair of simulations into low-dimensional space. Taking the distance between projected points provides a metric for determining the similarity between simulations. The smaller the distance, the more similar they are.

Once we have trained the Siamese network, we can perform a number of different analyses with it. The first example we show is with a four-species Lotka-Volterra model, with the base parameters tuned to create oscillatory behavior

**Figure 2**: Comparison of using a Siamese network to using a specified output for a sensitivity analysis. Sensitivities are normalized to the highest value. We see that while some parameters are ranked similarly, other parameters are ranked very differently. This is due to the differences in how the sensitivity output is measured.

**Figure 3**: Distributions for parameter values (top two rows) and specific outputs (bottom row) for clustered model simulations.

- Campbell, K., McKay, M. D. & Williams, B. J. Sensitivity analysis when model outputs are functions. Reliability Engineering & System Safety 91, 1468–1472 (2006).
- Lenhart, T., Eckhardt, K., Fohrer, N. & Frede, H.-G. Comparison of two different approaches of sensitivity analysis. Physics and Chemistry of the Earth, Parts A/B/C 27, 645–654 (2002).
- Li, D. & Finley, S. D. Mechanistic insights into the heterogeneous response to anti-VEGF treatment in tumors. Computational and Systems Oncology 1, e1013 (2021).
- Chicco, D. Siamese neural networks: An overview. Artificial Neural Networks 73–94 (2021).
- Hoffer, E. & Ailon, N. Deep metric learning using triplet network. in International workshop on similarity-based pattern recognition 84–92 (Springer, 2015).
- Vano, J., Wildenberg, J., Anderson, M., Noel, J. & Sprott, J. Chaos in low-dimensional Lotka–Volterra models of competition. Nonlinearity 19, 2391 (2006)
- Cess, C. G. & Finley, S. D. Multi-scale modeling of macrophage—T cell interactions within the tumor microenvironment. PLoS Computational Biology 16, e1008519 (2020)
- Tapinos, A. & Mendes, P. A method for comparing multivariate time series with different dimensions. PLoS ONE 8(2): e54201 (2013).

© 2023 - The Mathematical Oncology Blog