Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches

Let’s discuss: Why GPR-acceleration has failed to deliver on its promise, and how we finally fix it.

Being between disciplines, the discussion is also split.

ML Perspective

The Problem: Gaussian Process (GP) models are powerful but suffer from a well-known curse: the punishing cost of hyperparameter optimization. The need to invert a kernel matrix leads to cubic scaling with the number of training points. In on-the-fly scientific applications where data arrives sequentially, the time spent tuning the GP quickly becomes the primary bottleneck, making the entire approach impractical.

Our Solution: We solve this by decoupling the data used for prediction from the data used for hyperparameter tuning.

• FPS for Hyperparameters: Our core innovation is to perform the expensive hyperparameter optimization on a small, fixed-size subset of data. This subset is actively curated using Farthest Point Sampling (FPS), which ensures it remains representative even as the full dataset grows. This breaks the cubic scaling bottleneck.
• A Principled Metric: To make FPS effective for complex physical data (molecules), we use a distance metric based on Optimal Transport (the Earth Mover's Distance). It is permutation-invariant, allowing us to select a truly geometrically diverse subset from the point-cloud-like data.
• Stabilizing Training: We introduce data-driven guardrails, including an adaptive variance barrier and Hyperparameter Oscillation Detection (HOD), to ensure the optimization process remains stable even on this compact subset.
• vs. Other Methods: Unlike methods that use inducing points, our approach uses the full data history for the final prediction, ensuring no loss of accuracy.

The Impact: This "subset for tuning, full set for prediction" strategy makes the GP practical. We achieve a >2x speedup in wall-time over the previous state-of-the-art and drastically reduce model failure rates. It provides a general blueprint for creating efficient and robust surrogate models for expensive on-the-fly learning tasks.

Chemistry Perspective

The Problem: Finding saddle points (transition states) is crucial for understanding reaction mechanisms, but it's bottlenecked by the cost of quantum chemistry calculations. GPR-accelerated methods like GPDimer promised to reduce the number of these calculations, but they were often unstable and ultimately slower in total time-to-solution.

Our Solution: The OT-GP framework makes GPR acceleration a practical reality by fixing the source of these instabilities.

• A Chemically-Aware Metric: We introduce a permutation-invariant distance metric based on the Earth Mover's Distance. Unlike the previous D_1Dmaxlog metric, our EMD understands that identical atoms are interchangeable. It is not fooled by low-energy symmetric events like methyl rotations or proton transfers.
• Preventing Instability: This robust representation prevents the algorithm from adding redundant data to the training set, which was a primary cause of ill-conditioned kernel matrices and the catastrophic failures (e.g., exploding molecules) seen in older methods.
• Targeted Data Acquisition: We use this EMD with Farthest Point Sampling (FPS) to intelligently select data for hyperparameter tuning and an adaptive trust radius to guide the search, ensuring the model remains stable.

The Impact: On a benchmark of 238 reactions, OT-GP is a transformative improvement.

• Data Efficiency: We preserve the ~10x reduction in Hartree-Fock calculations compared to the standard Dimer method (median of ~28 vs. ~254).
• Wall-Time Speedup: We are >2x faster than the previous GPDimer (12.6 min vs. 28.3 min) and nearly 2x faster than the standard Dimer (12.6 min vs. 23.7 min).
• Reliability: We achieve a 96% success rate, solving cases where all previous methods failed.