Uncertainty derivative w.r.t atomic coordinates

[ghost]

I'm currently exploring the use of FLARE's uncertainty measure (e.g., predicted force variance) as a collective variable (CV) in molecular dynamics simulations, particularly in conjunction with Adaptive Biasing Force (ABF) or related enhanced sampling methods.

To implement this, I would need the derivative of the FLARE uncertainty with respect to atomic coordinates. I'm using FLARE integrated with LAMMPS (via LMPOTF) and would ideally want to compute these derivatives on the fly during MD runs to feed into my biasing protocol. Any advice or pointers to relevant parts of the codebase would be greatly appreciated

Questions:

1. Is it currently possible to compute or extract derivative using the existing FLARE or FLARE++ codebase?

2. If not, would you have any advice on how to implement this?

[YuuuXie]

Yes, there is the variance (uncertainty squared) implemented for all the predictions (including energy, forces, and stress):

flare/src/flare_pp/bffs/sparse_gp.cpp

Line 694 in b306fca

void SparseGP ::predict_DTC(Structure &test_structure) {

You can check the variance_efs there.

For python interface, you can use the variance_type to specify it

flare/flare/bffs/sgp/calculator.py

Line 61 in b306fca

elif self.gp_model.variance_type == "DTC":

[ghost]

This will give me the variance of forces/stress but what I need for my use case is the cartesian gradient of the uncertainty/CV this way i can define a bias force like this.

$$- \langle F_{\xi} \rangle_{z} = - \frac{1}{N_{\text{sampl}}(\xi = z)} \sum_{\substack{i=1 \ (\xi(x_i) = z)}}^{N_{\text{sampl}}} \mathbf{F}_i \cdot \frac{\nabla \xi(x_i)}{|\nabla \xi(x_i)|^2}$$

where $\xi(x)$ will be the uncertainty measure.

Again any advice on best way(if possible) to implement this using FLARE code base would be great