BUG: Repeated predictions from GP grow steadily slower (pytensor cache issue?)

Describe the issue:

I'm performing (offline) Bayesian Optimization using pymc Marginal GP. Maximizing the (expected improvement) acquisition function requires making repeated predictions of the GP mean and variance at various points in the data domain. But I've noticed this gets slower and slower as it proceeds. For instance, the first 50 calls take ~30 seconds but the first ~800 calls take ~10 minutes. I then re-fit a new, separate GP and maximize again. The next 800 calls take 19 minutes. Re-fit, re-maximize, 800 calls: 26 minutes. There are only 5 data points at the moment and two X dimensions (one y dimension), so it shouldn't be a data-scaling issue. Re-starting the Python session doesn't fix the issue, but re-starting the computer does.

I'm suspicious this is a pytensor cache issue. At one point I got a warning message WARNING (pytensor.link.c.cmodule): Deleting (Broken cache directory [EOF]): /home/john/.pytensor/compiledir_Linux-6.5--gcp-x86_64-with-glibc2.35-x86_64-3.11.4-64/tmpe71kqgp0. Curious, I looked at that ./pytensor/compileddir... directory mid-run, and and the ~1200 sub-directories comprise 380 MB and growing. There also seems to be an accumulation in RAM overhead, though that's harder to quantify (but on the order of 20-30 GB of RAM in use while the VM is idle after a week or two of this kind of workflow). Is pytensor scanning this cache with every call to predict? Any ideas how to avoid this, or stop it from slowing things down?

Reproduceable code example:

# Sorry, I know this isn't an actual reproducible example, I'll work on putting one together.

import pymc as pm
from tqdm.auto import trange

def define_GP_model(...):
    ...
    gp = pm.gp.Marginal(...)
    return model, gp

def fit_GP(model):
    ...
    with model:
        MAP = pm.find_MAP()

for _ in trange(1000):
    gp.predict(
                [16x2 array], point=MAP, diag=True, pred_noise=True
            )


for _ in trange(1000):
    gp.predict(
                [16x2 array], point=MAP, diag=True, pred_noise=True
            )


for _ in trange(1000):
    gp.predict(
                [16x2 array], point=MAP, diag=True, pred_noise=True
            )

Error message:

No response

PyMC version information:

pymc: 5.8.2
pymc-base: 5.12.0
pytensor: 2.16.3
pytensor-base: 2.19.0

Linux OS, pymc installed via mamba/conda

Context for the issue:

No response

Start with the repeated gp.predict calls in the provided example and turn the placeholder inputs into a minimal reproducible case. Monitor the PyTensor compiledir contents and memory while repeating predictions, then trace whether cache growth or compilation causes the slowdown. Done means the cause is isolated and a regression test or documented workaround is identified.