Add general integer exponents #128

kvhuguenin · 2024-12-16T16:08:08Z

Add exponents >3 to the main branch.
The core changes in the potential have already been implemented.
The most important change that still has to be implemented and tested in the rest of the code is that exponent now is of data type int rather than float.
Also, we need some good unit tests. I was thinking of a combination of regression tests for some of the more complicated structures + generalized Madelung constants that I have computed in the past with a different code.

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CHANGELOG updated with public API or any other important changes?

📚 Documentation preview 📚: https://torch-pme--128.org.readthedocs.build/en/128/

PicoCentauri

As test I would just do a regression test for the function.

PicoCentauri · 2024-12-18T13:19:50Z

src/torchpme/potentials/inversepowerlaw.py

@@ -17,6 +17,27 @@ def gamma(x: torch.Tensor) -> torch.Tensor:
    return torch.exp(gammaln(x))


+# Auxilary function for stable Fourier transform implementation
+def gammainc_upper_over_powerlaw(exponent, zz):


Give the equation in the docstring here.

src/torchpme/potentials/inversepowerlaw.py

E-Rum

Looks good, but there are some things that need to be double-checked. I will continue updating the tests once we fix them.

E-Rum · 2024-12-20T12:12:36Z

src/torchpme/potentials/inversepowerlaw.py

+    if exponent == 2:
+        return torch.sqrt(torch.pi / zz) * torch.erfc(torch.sqrt(zz))
+    if exponent == 3:
+        return -torch.expi(-zz)


As far as I know torch.expi doesn't exist in torch module ...

E-Rum · 2024-12-20T12:16:57Z

src/torchpme/potentials/inversepowerlaw.py

+def gammainc_upper_over_powerlaw(exponent, zz):
+    if exponent not in [1, 2, 3, 4, 5, 6]:
+        raise ValueError(f"Unsupported exponent: {exponent}")
+
+    if exponent == 1:
+        return torch.exp(-zz) / zz
+    if exponent == 2:
+        return torch.sqrt(torch.pi / zz) * torch.erfc(torch.sqrt(zz))
+    if exponent == 3:
+        return -torch.expi(-zz)
+    if exponent == 4:
+        return 2 * (
+            torch.exp(-zz) - torch.sqrt(torch.pi * zz) * torch.erfc(torch.sqrt(zz))
+        )
+    if exponent == 5:
+        return torch.exp(-zz) + zz * torch.expi(-zz)
+    if exponent == 6:
+        return (
+            (2 - 4 * zz) * torch.exp(-zz)
+            + 4 * torch.sqrt(torch.pi) * zz**1.5 * torch.erfc(torch.sqrt(zz))
+        ) / 3
+
+


Can we double-check that everything here is correct? With the new implementation, test_values_ewald.py fails for inverse potentials with an exponent of 1, as it does not coincide with the Madelung constant.

E-Rum · 2024-12-26T00:44:18Z

The current status is as follows:

For arbitrary odd integer exponents ( p >=3 ), we need the exponential integral, which is not implemented in PyTorch. The current solution is to use the existing SplinedPotential to model 1/r^p type potentials. However, before fully adopting it, I plan to use the scipy module, which includes the exponential integral, to verify that the values generated by SplinedPotential are consistent with the theoretical ones.

However, there is a specific issue when p = 3. In this case, certain variables become degenerate, leading to situations where we raise values to the power of zero and even encounter division by zero (e.g. background_correction function).

Can someone provide insights into this issue and suggest potential solutions?

…functions in the InversePowerLawPotential class

E-Rum · 2025-01-03T14:12:14Z

In the last commit, I made the following changes:
I temporarily inserted a SciPy function that contains the exponential integral into the existing InversePowerLawPotential class. Even though this breaks PyTorch differentiability, it temporarily allows us to have a reference value.

As discussed with @ceriottm, one possible solution to overcome the absence of the exponential integral in PyTorch is to implement it using a spline potential. Therefore, I also drafted how this could be implemented in a separate integerspline.py module.

So far, the numerically splined implementation coincides with the reference SciPy one with good accuracy.

However, we still need to discuss what to do with p <= 3. From what I found in the literature, our current implementation is correct for p>3. However, for p<=3, one should be careful as certain constraints (e.g., charge or dipole neutrality) need to be enforced (this is apperently why we are having trouble right now in the code with p = 3). Please correct me if I misinterpreted this while reviewing the literature.

If that’s the case, I think we should add some constraints in the code for the above-mentioned exponents.

ceriottm · 2025-01-05T06:09:08Z

In the last commit, I made the following changes: I temporarily inserted a SciPy function that contains the exponential integral into the existing InversePowerLawPotential class. Even though this breaks PyTorch differentiability, it temporarily allows us to have a reference value.

As discussed with @ceriottm, one possible solution to overcome the absence of the exponential integral in PyTorch is to implement it using a spline potential. Therefore, I also drafted how this could be implemented in a separate integerspline.py module.

So far, the numerically splined implementation coincides with the reference SciPy one with good accuracy.

However, we still need to discuss what to do with p <= 3. From what I found in the literature, our current implementation is correct for p>3. However, for p<=3, one should be careful as certain constraints (e.g., charge or dipole neutrality) need to be enforced (this is apperently why we are having trouble right now in the code with p = 3). Please correct me if I misinterpreted this while reviewing the literature.

If that’s the case, I think we should add some constraints in the code for the above-mentioned exponents.

The idea of the "background correction" is to add a uniform density that cancels out the total pseudocharge making the system overall neutral. I see no reason why this wouldn't be doable for p=2,3 so there might be an error in the expression for p=3

E-Rum · 2025-01-06T13:11:08Z

This is from
Williams, D. E. (1989). Accelerated Convergence Treatment of R−n Lattice Sums. Crystallography Reviews, 2(1), 3–23. https://doi.org/10.1080/08893118908032944

Thus, there are indeed some restrictions for p<3, which might be causing the divergences. Alternatively, I might have misunderstood the issue, and we may have implemented the background_correction incorrectly.

…ort backpropagation

E-Rum · 2025-01-06T19:26:13Z

Okay, implementing a custom backpropagation-compatible PyTorch exponential integral turned out to be not that hard(thanks @kvhuguenin for noticing it), so it’s done. Now, we need to resolve the background_correction problem and add tests. I will add tests soon to compare the values and derivatives of the InversePowerLawPotential with the splined implementation.

…or new exponent values

E-Rum · 2025-01-08T16:54:46Z

I added tests to compare theoretical values and their derivatives with the splined potential for exponents 4, 5, and 6. I also decided to delete the SplinedInteger potential, as it has become redundant now that we have theoretical backpropagatable integer potentials. The only thing left to check is the background correction and what’s happening with p = 3 , and then it will be ready to merge.

PicoCentauri

Awesome!

src/torchpme/potentials/inversepowerlaw.py

…r consistency with SciPy

…Compatibility with Potentials (#143) * Refactor parameter handling in calculators and potentials for improved dtype and device management * Updated docstrings and changelog, added an assertion to check for an instance of the potential, and resolved the TorchScript Potential/Calculator incompatibility. * Update changelog and add test for potential and calculator compatibility

PicoCentauri

Very nice. I have just a suggestion to keep the repo a bit clean.

Thanks @E-Rum !

src/torchpme/potentials/inversepowerlaw.py

…th.py script

Add general integer exponents up to 6

d67ff35

PicoCentauri reviewed Dec 18, 2024

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PicoCentauri assigned E-Rum Dec 18, 2024

ceriottm mentioned this pull request Dec 19, 2024

PME for Magnetostatics #54

Open

E-Rum added 2 commits December 20, 2024 11:01

Merge branch 'main' into exponents

d2dccf0

Updated helper function for new Vesin version, started to change tests

ad9f194

E-Rum reviewed Dec 20, 2024

View reviewed changes

Add the InversePowerLawPotentialSpline class and use temporary SciPy …

1d2ed8a

…functions in the InversePowerLawPotential class

Linted + added a custom PyTorch exponential integral function to supp…

54b6fd6

…ort backpropagation

ceriottm mentioned this pull request Jan 8, 2025

SplinePotential device compatibility #138

Merged

E-Rum added 3 commits January 8, 2025 14:35

Merge branch 'main' into exponents

401e65d

Checkpoint with working tests and linting

738c8e9

Remove unused InversePowerLawPotentialSpline class and update tests f…

60be4ac

…or new exponent values

PicoCentauri reviewed Jan 9, 2025

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src/torchpme/potentials/inversepowerlaw.py Outdated Show resolved Hide resolved

src/torchpme/potentials/inversepowerlaw.py Outdated Show resolved Hide resolved

E-Rum and others added 7 commits January 9, 2025 15:08

Add wrapper around class, restructure if-else condition, add tests fo…

cbf8d3b

…r consistency with SciPy

Fix linting issues caused by the new ruff version

323c920

Another lint

cff0039

Added a condition for background correction and updated the changelog

60dcade

Lint

2418c37

Merge branch 'main' into exponents

f077ba6

E-Rum marked this pull request as ready for review January 17, 2025 11:21

E-Rum requested a review from PicoCentauri January 17, 2025 11:26

E-Rum mentioned this pull request Jan 17, 2025

Update lr_from_k_sq Function to Handle k_sq → 0 Limit for Exponents > 3 #144

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PicoCentauri reviewed Jan 17, 2025

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src/torchpme/potentials/inversepowerlaw.py Outdated Show resolved Hide resolved

Moved mathematical functions from inversepowerlaw.py to a separate ma…

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…th.py script

PicoCentauri approved these changes Jan 17, 2025

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Move test

0f8d7e5

E-Rum merged commit 3540a81 into main Jan 17, 2025
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E-Rum deleted the exponents branch January 17, 2025 15:33

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Add general integer exponents #128

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