Scaling Gaussian Process Regression with Full Derivative Observations
This enables more efficient derivative-aware Gaussian Process modeling for high-dimensional scientific applications like molecular force fields, though it's an incremental extension of existing work.
The authors tackled the problem of scaling Gaussian Process regression with full derivative observations by developing DSoftKI, which extends SoftKI's kernel approximation to incorporate derivative information through directional orientation of interpolation points. They demonstrated DSoftKI's accuracy on synthetic benchmarks and molecular force field prediction in 100-1000 dimensions, showing it can scale to larger datasets with full derivative observations than previously possible.
We present a scalable Gaussian Process (GP) method that can fit and predict full derivative observations called DSoftKI. It extends SoftKI, a method that approximates a kernel via softmax interpolation from learned interpolation point locations, to the setting with derivatives. DSoftKI enhances SoftKI's interpolation scheme to incorporate the directional orientation of interpolation points relative to the data. This enables the construction of a scalable approximate kernel, including its first and second-order derivatives, through interpolation. We evaluate DSoftKI on a synthetic function benchmark and high-dimensional molecular force field prediction (100-1000 dimensions), demonstrating that DSoftKI is accurate and can scale to larger datasets with full derivative observations than previously possible.