Physics informed Gaussian Processes

A lot of sensor and other physically observed data obey underlying Physics. These can be modeled by stochastic differential equations (SDEs)[1]. Such tools are interpretable, flexible and also acts as a bridge to multiple aspects of Bayesian learning like State Space Models (SSMs) and Gaussian processes (GPs)[2]. Thesis topics will deal with exploiting these relations to solve tasks related to signal processing and machine learning. Example topics can be as follows:

1) Efficient learning of Gaussian processes which obey specific SDEs [3]

2) Enhancing GP performance by combining multiple physics driven kernels and interpreting the results

3) Studying more involved SDEs (nonlinear etc) by approximation and related GPs [1]

4) Apply SDEs on more irregular domains like graphs and hypergraphs

This work will be in collaboration with Dr. Bishwadeep Das.

References

[1] Särkkä, S., & Solin, A. (2019). Applied stochastic differential equations (Vol. 10). Cambridge University Press.

[2] Williams, C. K., & Rasmussen, C. E. (2006). Gaussian processes for machine learning (Vol. 2, No. 3, p. 4). Cambridge, MA: MIT press.

[3] Nikitin, A. V., John, S. T., Solin, A., & Kaski, S. (2022, May). Non-separable spatio-temporal graph kernels via SPDEs. In International Conference on Artificial Intelligence and Statistics (pp. 10640-10660). PMLR.

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Last modified: 2025-09-29