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REVIEW 4 major objections 5 minor 38 references

Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filters to 3D UNETs

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Denoising with a DFT-residual variance stabilization cuts required DMC sampling by 10–100x.

desk verdict Useful variance-stabilizing transform and a careful benchmark, but the 10-100x speedup metric conflates denoiser bias with sampling noise and needs reframing. read the letter →

arxiv 2608.08152 v1 pith:DI2THNJI submitted 2026-08-08 cond-mat.mtrl-sci quant-ph

Kenneth O. Berard , Brenda Rubenstein , Jaron T. Krogel This is my paper · ORCID
classification cond-mat.mtrl-sciquant-ph
keywords DiffusionMonteCarloelectrondensitydenoisingvariancestabilizationJensen-ShannondivergenceSmoothNfunctionaltheoryprior3DUNETquantum
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Diffusion Monte Carlo (DMC) produces benchmark-quality electron densities but with substantial statistical noise that makes them hard to use. This paper argues that a variance-stabilizing transformation, built around the density functional theory (DFT) density as a physical prior, turns the QMC noise into a form that standard denoisers can remove without destroying the signal. The authors compare Fourier filtering, image-style denoisers, and 3D regression and deep-learning models across diamond, blue phosphorus, and vanadium dioxide. They find that a regularized 3D regression smoother (SmoothN) is the most consistent, beating raw QMC sampling by an effective factor of 10–100x in the sampling budget needed to reach a target density accuracy.

What carries the argument

The central object is the residual variance-stabilizing transform $u_{\rm noisy}(\mathbf{r}) = [\rho_{\rm noisy}(\mathbf{r})-\rho_{\rm DFT}(\mathbf{r})]/\sqrt{\rho_{\rm DFT}(\mathbf{r})+\epsilon}$, which maps heteroscedastic Poisson-like QMC noise onto a near-uniform Gaussian field so that denoisers designed for additive white noise can operate. The argument is carried by combining this transform with the SmoothN penalized least-squares smoother, which minimizes a data-fidelity term plus a second-order Laplacian penalty, using a fast DCT diagonalization and iteratively reweighted least squares to suppress outliers. The evaluation machinery is the Jensen-Shannon divergence and its low-noise asymptotic formula $D_{JS}(p_{\rm noisy},p_{\rm exact}) \approx \frac{1}{8\log 2}\frac{M}{N}$, which lets the authors subtract the reference's residual noise and convert denoised divergences into effective sample counts and speedups.

What would settle it

Take a noisy low-sample DMC density, denoise it, and compare the denoised result against an essentially exact reference (for example, a post-Hartree-Fock density on a small molecule). If the denoised density is closer to the DFT prior than to the exact many-body reference in regions where DFT is known to fail, the speedup estimate would be inflated and the method's suitability for functional inversion would be undermined.

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Extended reading notes

Core claim

The central claim is that properly conditioned denoising can extract smooth, physically accurate electron densities from noisy DMC runs that closely match highly converged references, with the best regression methods performing best in both high- and low-noise limits for all three materials. The conditioning step is the load-bearing move: instead of denoising the raw density, the authors transform it as $(\rho_{\rm noisy}-\rho_{\rm DFT})/\sqrt{\rho_{\rm DFT}+\epsilon}$, which makes the residual noise approximately homoscedastic and slowly varying. In this space a penalized least-squares spline (SmoothN) reduces the Jensen-Shannon divergence to the exact density so effectively that the authors' asymptotic formula converts the improvement into an effective 10–100x reduction in Monte Carlo samples required for a given density fidelity. The paper also shows that 2D image-based models produce slicing artifacts, that the square-root transform helps but underperforms the residual transform, and that the denoising curves for different materials collapse onto shared scaling laws when plotted against samples per voxel.

Load-bearing premise

The speedup metric converts reduced Jensen-Shannon divergence into an effective sample count by assuming the denoised density's remaining error behaves like Poisson shot noise from a larger sample, so if a denoiser also biases the density toward the DFT prior, the claimed sampling savings overstate what a true longer QMC run would give.

Editorial extensions

If this is right

  • Density-generating DMC runs targeting a fixed density accuracy can be shortened by one to two orders of magnitude, since the denoiser supplies the remaining statistical fidelity.
  • The variance-stabilized regression pipeline transfers across the three tested materials and across VMC and DMC, with the divergence clustering on samples per voxel rather than on the material.
  • Denoised densities stay below the DFT baseline divergence, meaning they retain QMC many-body information instead of collapsing to the DFT prior.
  • 2D and flattened models remain viable for statistical reduction but introduce nonphysical slicing artifacts, so volumetric methods are the safe default for downstream use.
  • The approach opens a practical route to feeding smooth, near-benchmark densities into DFT functional inversion and other noise-sensitive analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The 10–100x speedup is an upper bound if denoisers trade variance for bias: a denoiser that pulls the density toward the DFT prior will lower the JSD without representing true sampling savings, since the metric assumes the residual error is pure Poisson shot noise.
  • The method's dependence on a DFT prior means it may systematically suppress correlation-driven density features that differ sharply from DFT; testing on a system with a strong DFT-versus-QMC density disagreement would clarify the bias ceiling.
  • One testable extension is to run the same residual transform with the DFT prior deliberately corrupted, and measure how much of the speedup survives, which would isolate how much of the gain is physical conditioning versus prior information.
  • The observed power-law speedup decay at high sampling suggests diminishing but still substantial returns even at 500 billion samples per voxel, so the approach should be validated at yet higher sampling on a small cell where an essentially exact reference exists.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a post-processing pipeline for reducing statistical noise in diffusion Monte Carlo (DMC) electron densities. The key ingredient is a variance-stabilizing transform based on the residual between the noisy density and a DFT reference density, followed by denoising in a nearly homoscedastic space. The authors compare Fourier filtering, BM4D/BM3D, local polynomial regression, SmoothN penalized least squares, a 3D UNET, and SCUNET on diamond, blue phosphorus, and rutile VO2, using the Jensen-Shannon divergence (JSD) to a high-sampling DMC reference as the fidelity metric. They report that regression methods, especially SmoothN, are the most consistent across materials and noise regimes, and translate the JSD reductions into effective sampling speedups of 10-100x via a Poisson shot-noise asymptotic formula.

Significance. If the central speedup claim were rigorously established, the work would be practically significant: it would lower the sampling cost for obtaining smooth QMC densities, which are inputs to DFT functional inversion and other noise-sensitive downstream tasks. The paper has clear strengths: a physically motivated variance-stabilizing transform; a broad comparison of classical and learning-based denoisers; a synthetic training pipeline that avoids expensive QMC training data; and a systematic evaluation across three chemically distinct materials. The information-theoretic JSD metric is appropriate for probability-like densities, and the asymptotic derivation in the supplementary material is internally consistent under its stated independence assumptions. However, the headline 10-100x speedup rests on identifying any JSD reduction with an equivalent increase in Poisson sample count, which conflates systematic denoiser bias with noise reduction. Because the bias-variance decomposition is never performed, the quantitative claim is not yet supported.

major comments (4)
  1. [Sec. IV, Eqs. (18)-(20); SI Sec. I] The speedup definition S = N_eff/N_mc assumes that the denoised density differs from the exact density only by zero-mean Poisson shot noise, so that D_JS(p_DN, p_exact) = M/(8 ln 2 N_eff). In the residual variance-stabilized space u = (rho_noisy - rho_DFT)/sqrt(rho_DFT), all of the tested denoisers shrink residuals toward zero, so the expected denoised density E[p_DN] is biased toward the DFT density. The measured JSD therefore contains a bias contribution proportional to sum_m (E[p_DN,m] - p_exact,m)^2 / p_m in addition to the variance term. The paper itself acknowledges 'template bias' in the Conclusion, but never quantifies it; the only check in SI Sec. V is a visual isosurface comparison, which cannot separate bias from variance. Consequently, the reported speedup S may largely reflect systematic shrinkage toward the DFT prior rather than a genuine reduction in required QMC sampling. This is load-bearing because the 10-100x speedup is the central quantitative contribution and the stated justification for downstream applications. I recommend decomposing the JSD into variance and bias components, or at minimum applying each denoiser to very high-sample inputs (where statistical noise is negligible) and measuring the residual to the reference to bound the bias contribution.
  2. [Sec. IV, 'Divergence and Speedup vs. Samples for Hyperparameter-Tuned Denoisers'] The manuscript states that hyperparameters 'explicitly minimize the D_JS at each discrete sampling level,' using the same high-sampling reference that is then used to evaluate the JSD and compute speedups. This makes the method ranking in Figs. 5 and 6 partly self-fulfilling: for example, SmoothN's 0.81 worst-case score in Fig. 6 is the result of test-set optimization rather than an out-of-sample assessment. The synthetic training pipeline already provides a natural source of training data; a proper split (e.g., train/validation/test, or nested cross-validation over the per-sampling-level hyperparameters) is needed before the claim that 'regression methods outperform all others across all materials' can be accepted. This is a load-bearing issue because the final recommendation of SmoothN as the most robust denoiser rests on these rankings.
  3. [Sec. III, 'Fourier Transform Filtering and Augmentation'] The FFT augmented variant is described as replacing filtered spectral components with 'pristine reference amplitudes.' If that pristine reference is the high-sampling DMC density later used as the JSD target in Sec. IV, then this variant is circular by construction: it injects the evaluation target directly into the denoised output, so its competitive or superior JSD does not demonstrate denoising capability. The manuscript must specify what the pristine reference is. If it is the DFT density, then the method is not circular but it is injecting DFT information, which should be accounted for in the bias analysis and in the interpretation of 'surpassing the DFT baseline.' Either way, the current presentation is ambiguous and the variant's performance should be either justified or removed from the ranking.
  4. [Sec. II, Eq. (13) and SI Sec. I] The asymptotic correction D_JS(p_DN, p_exact) ≈ D_JS(p_DN, p_noisy) − M/(8 ln 2 N_mc) is derived in the SI for two independent noisy histograms with the same noise-free mean. Here p_DN is a deterministic function of p_noisy (the output of a denoiser applied to that same noisy density), not an independent sample, and its mean may differ from the exact density because of denoiser bias. The subtraction therefore does not follow from the SI derivation, and the error in this approximation can be of the same order as the speedup being computed. This affects every speedup reported in Figs. 5-7. Please either provide a revised derivation that accounts for the correlation between p_DN and p_noisy, or explicitly treat Eq. (13) as an uncontrolled approximation and quantify its uncertainty.
minor comments (5)
  1. [Abstract and Fig. 5] The abstract states that the best denoisers reduce the required cost by 10-100x, but the speedup plots in Fig. 5 show strong dependence on sampling level and material, with some methods falling below 1x at high sample counts. Please qualify the claim as peak or best-case, and state the range of sampling levels and materials over which it holds.
  2. [Sec. II, Eq. (7)] The square-root transform takes the absolute value of rho_noisy before applying the square root. In very low-density regions where statistical noise can produce negative density values, this introduces a positive bias that is not discussed; its effect on the JSD should be mentioned or quantified.
  3. [Sec. II, 'Materials and Datasets'] The ICSD collection codes are given as 'ICSD-25253' and 'ICSD-1504'; standard ICSD codes are six-digit numbers (e.g., 25253 is five digits). Please verify these identifiers and provide the correct collection codes or explicit references to the structure sources.
  4. [Sec. II, Poisson model] The Poisson model in Eqs. (4)-(6) treats successive walker configurations as independent. In DMC, configurations are serially correlated, so the effective sample size is smaller than the raw number of walker configurations N_mc. This affects the interpretation of the absolute speedup (though not the relative comparison of denoisers); a brief discussion or a correction factor would strengthen the quantitative claims.
  5. [SI Fig. S1] The caption of Fig. S1 does not specify which material or sampling range is shown, and the label 'Analytical VST' is undefined in the main text. Please add the missing details and define the acronym.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor oracle construction in the FFT-augmented variant for no-Jastrow VMC; central DMC denoising claims remain independent.

  1. self definitional [Section III (Fourier Transform Filtering and Augmentation); Materials and Datasets; Figure 3]
    "VMC was also performed without a trial Jastrow-factor. In that case, the noise-free limit of the electron density is identical to the DFT density. ... The noisy spectral components beyond this cutoff are either removed (zeroed) or replaced with the pristine reference amplitudes (augmented). ... [Supplementary] replaced by their corresponding density functional theory (DFT) spectral amplitudes."

    For the no-Jastrow VMC datasets, the paper states that the noise-free limit of the electron density equals the DFT density, so the evaluation reference is the DFT density. The augmented FFT variant replaces the filtered high-frequency Fourier components with DFT spectral amplitudes, i.e., with the Fourier amplitudes of the very reference against which the denoised density is scored. The resulting low JSD (e.g., 1.82e-04 for FFT in Figure 3) is therefore guaranteed by construction: the estimate contains target Fourier modes injected directly.

full rationale

The central derivation chain of the paper is otherwise self-contained. The denoising comparison is benchmarked against high-sample DMC references generated externally to the denoisers, and the main ranking (SmoothN best, BM4D second) is based on those DMC references rather than on any quantity fed back into the methods. The variance-stabilizing residual transform uses the DFT density as a physical prior, but the paper explicitly checks denoised results against the DFT baseline and requires that useful denoisers surpass that baseline, which prevents the transform from being a purely circular prior collapse for the DMC claims. The speedup metric (Eqs. 18-20) does assume that a denoised density's residual deviation is equivalent to Poisson shot noise; that is an unvalidated statistical-equivalence assumption and a genuine validity risk, especially because the paper's own conclusion flags 'template bias,' but it is not a circular reduction: the speedup is defined from the measured JSD rather than being an input to it. The only identifiable construction-like step is the augmented FFT variant when applied to the no-Jastrow VMC densities, whose reference is identical to the DFT density whose spectral amplitudes the method injects. That step is not central to the paper's main conclusions. Overall, the derivation is substantially independent of its inputs, and the observed circularity is minor and localized.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are mostly in the synthetic training pipeline and in the per-sampling-level hyperparameter tuning; the main evaluation assumption is that JSD reductions can be converted to effective sample counts.

free parameters (5)
  • Synthetic Gaussian spread sigma = 6.0 voxels
    Chosen by hand for the synthetic density training data; affects the spatial correlation scale the UNET learns.
  • Perturbation strength s = random in [0.05, 0.15]
    Random strength for the physics-aware perturbation in the synthetic pipeline; a generative modeling choice, not fitted to target data.
  • SmoothN hyperparameters = tuned per sampling level
    The paper states hyperparameters explicitly minimize D_JS at each sampling level, i.e., tuned against the reference density.
  • Fourier cutoff / variance ceiling = dynamic per density
    The cutoff is determined by a variance-ceiling function on spectral amplitudes; the threshold selection is data-dependent.
  • Hubbard U for VO2 = 3.5 eV
    Taken from prior QMC benchmark literature [27], used for the LDA+U reference density.
assumptions (5)
  • domain assumption QMC density histogram cell counts are independent Poisson variates with mean N_mc * rho_m.
    Used to derive the JSD asymptotics (Eqs. 11-13) and the variance-stabilizing transform; DMC walkers are serially correlated, so the effective sample count may differ from N_mc.
  • domain assumption The DFT density is a sufficiently accurate structural proxy so that rho_QMC/rho_DFT ~ 1 in the transformed noise variance.
    Invoked in the residual transformation (Eq. 8) and in the supplementary 'Estimating Sigma' section to justify homoscedasticity.
  • domain assumption The low-noise asymptotic JSD formula remains valid at moderate sample counts and for denoised densities whose errors may be systematic rather than Poisson shot noise.
    Used to apply the N_ref correction (Eq. 13) and to convert JSD to effective sample count (Eqs. 18-20).
  • domain assumption Synthetic Gaussian-mixture densities with Poisson noise transfer to real QMC densities of diamond, blue phosphorus, and VO2.
    The UNET and SCUNET are trained only on synthetic data; the paper assumes the learned noise model generalizes to physical densities.
  • standard math Jensen-Shannon divergence on normalized histograms is a faithful fidelity metric for electron densities.
    Standard information-theoretic divergence; the authors justify its use over KL, which diverges in vacuum regions.

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Cite this review

Pith. "Pith review of Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filters to 3D UNETs." pith.science (2026). https://pith.science/paper/DI2THNJI

@misc{pith2026260808152,
  author       = {Pith},
  title        = {Pith review of: Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filters to 3D UNETs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DI2THNJI}},
  note         = {Machine review of arXiv:2608.08152}
}
read the original abstract

Obtaining accurate electron densities is important for the fundamental description of molecular and condensed matter systems, as well as for the development of next-generation density functionals. Diffusion Monte Carlo (DMC), in particular, is known to produce benchmark-quality data; however, the predicted real-space electron densities contain substantial amounts of statistical noise. In this work, we study denoising approaches for DMC densities, judged on the basis of the information-theoretic Jensen-Shannon divergence. The denoising is facilitated by an approximate heteroscedastic to homoscedastic transformation leveraging the density functional theory density as a physical prior. We systematically compare a range of denoising techniques-including Fourier transform, regression, and 3D UNETs-on materials showing a wide range of density variations: carbon diamond, blue phosphorus, and rutile VO2. Our results indicate that simple flattened machine learning models and 2D image-based models introduce line artifacts and struggle to capture the full spatial correlation. In contrast, when using variance stabilization, regression methods outperform all others in both the high and low- noise limits across all materials considered. The best denoisers reduce the required cost of density-generating DMC simulations by 10-100x, providing a promising route forward for application in noise-sensitive tasks such as DFT functional inversion.

Figures

Figures reproduced from arXiv: 2608.08152 by the authors.

Figure 1
Figure 1. FIG. 1: Denoised isosurfaces of low-sample DMC electron densities for diamond, blue phosphorus, and [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Direct JSD comparison for different [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Visual comparison of a cross-sectional [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Divergence of the denoised densities generated using BM4D with different density transformations [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Divergences (left) and speedup (right) of denoised densities produced using hyper-tuned denoisers [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Performance scores computed for each [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Performance of the SmoothN denoiser across all materials in terms of divergence (left) and speedup [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

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Works this paper leans on

38 extracted references · 32 canonical work pages

  1. [1]

    & Kohn, W

    Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev.136, B864–B871 (1964). URLhttps://link.aps.org/doi/10. 1103/PhysRev.136.B864

    work page 1964

  2. [2]

    Atoms in Molecules: A Quantum Theory

    Bader, R. Atoms in Molecules: A Quantum Theory. International series of monographs on chemistry (Clarendon Press, 1990). URLhttps://books. google.com/books?id=up1pQgAACAAJ

    work page 1990

  3. [3]

    Complexity in strongly corre- lated electronic systems

    Dagotto, E. Complexity in strongly corre- lated electronic systems. Science309, 257– 262 (2005). URLhttps://www.science. org/doi/abs/10.1126/science.1107559. https://www.science.org/doi/pdf/10.1126/science.1107559

    doi:10.1126/science.1107559 2005

  4. [4]

    & Tokura, Y

    Imada, M., Fujimori, A. & Tokura, Y . Metal- insulator transitions. Rev. Mod. Phys.70, 1039– 1263 (1998). URLhttps://link.aps.org/doi/ 10.1103/RevModPhys.70.1039

    doi:10.1103/revmodphys.70.1039 1998

  5. [5]

    & Hermansson, K

    Coppens, P. & Hermansson, K. X-ray charge den- sities and chemical bonding. Physics Today51, 66 (1998)

    work page 1998

  6. [6]

    Genoni, A. et al. Quantum crystallography: Current developments and future perspectives. Chemistry – A European Journal24, 10881–10905 (2018)

    work page 2018

  7. [7]

    & Sham, L

    Kohn, W. & Sham, L. J. Self-consistent equa- tions including exchange and correlation ef- fects. Phys. Rev.140, A1133–A1138 (1965). URLhttps://link.aps.org/doi/10.1103/ PhysRev.140.A1133

    work page 1965

  8. [8]

    Perdew, J. P. & Schmidt, K. Jacob’s ladder of density functional approximations for the exchange- correlation energy (2001). URLhttps://api. semanticscholar.org/CorpusID:93552655

    work page 2001

Show all 38 references
  1. [9]

    density func- tional theory is straying from the path toward the exact functional

    Kepp, K. P. Comment on “density func- tional theory is straying from the path toward the exact functional”. Science356, 496– 496 (2017). URLhttps://www.science. org/doi/abs/10.1126/science.aam9364. https://www.science.org/doi/pdf/10.1126/science.aam9364

    2017 doi

  2. [10]

    & Burke, K

    Kim, M.-C., Sim, E. & Burke, K. Understanding and reducing errors in density functional calcula- 19 tions. Phys. Rev. Lett.111, 073003 (2013)

    2013

  3. [11]

    Ceperley, D. M. & Alder, B. J. Ground state of the electron gas by a stochastic method.Phys. Rev. Lett. 45, 566–569 (1980). URLhttps://link.aps. org/doi/10.1103/PhysRevLett.45.566

    1980 doi

  4. [12]

    Foulkes, W. M. C., Mitas, L., Needs, R. J. & Rajagopal, G. Quantum monte carlo sim- ulations of solids. Rev. Mod. Phys.73, 33–83 (2001). URLhttps://link.aps.org/doi/10. 1103/RevModPhys.73.33

    2001

  5. [13]

    On the eigenfunctions of many- particle systems in quantum mechanics

    Kato, T. On the eigenfunctions of many- particle systems in quantum mechanics. Communications on Pure and Applied Mathematics 10, 151–177 (1957)

    1957

  6. [14]

    On the correlation problem in atomic and molecular systems

    ˇCížek, J. On the correlation problem in atomic and molecular systems. calculation of wavefunction components in ursell-type expan- sion using quantum-field theoretical methods. The Journal of Chemical Physics45, 4256–4266 (1966). URLhttps://doi.org/10.1063/1. 1727484

    1966 doi

  7. [15]

    & Caffarel, M

    Assaraf, R. & Caffarel, M. Zero-variance prin- ciple for monte carlo algorithms. Phys. Rev. Lett. 83, 4682–4685 (1999). URLhttps://link.aps. org/doi/10.1103/PhysRevLett.83.4682

    1999 doi

  8. [16]

    & Umrigar, C

    Toulouse, J., Assaraf, R. & Umrigar, C. J. Zero- variance zero-bias quantum monte carlo estimators of the spherically and system-averaged pair den- sity. The Journal of Chemical Physics126, 244112 (2007)

    2007

  9. [17]

    & Wasserman, A

    Shi, Y . & Wasserman, A. Inverse kohn–sham density functional theory: Progress and challenges. The Journal of Physical Chemistry Letters12, 5308–5318 (2021). URLhttps://doi.org/10. 1021/acs.jpclett.1c00752. PMID: 34061541, https://doi.org/10.1021/acs.jpclett.1c00752

    2021 doi

  10. [18]

    & Gavini, V

    Kanungo, B., Zimmerman, P. & Gavini, V . Ex- act exchange-correlation potentials from ground- state electron densities. Nature Communications10, 4497 (2019)

    2019

  11. [19]

    & Fatemi, E

    Rudin, L., Osher, S. & Fatemi, E. Non- linear total variation based noise removal algo- rithms. Physica D: Nonlinear Phenomena60, 259– 268 (1992)

    1992

  12. [20]

    & Egiazar- ian, K

    Dabov, K., Foi, A., Katkovnik, V . & Egiazar- ian, K. Image denoising by sparse 3- d transform-domain collaborative filtering. IEEE Transactions on Image Processing16, 2080– 2095 (2007)

    2007

  13. [21]

    & Foi, A

    Maggioni, M., Katkovnik, V ., Egiazarian, K. & Foi, A. Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Transactions on Image Processing22, 119– 133 (2013)

    2013

  14. [22]

    & Brox, T

    Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015, 234–241 (Springer International Publishing, Cham, 2015)

    2015

  15. [23]

    S., Brox, T

    Çiçek, Ö., Abdulkadir, A., Lienkamp, S. S., Brox, T. & Ronneberger, O. 3d u-net: Learn- ing dense volumetric segmentation from sparse annotation. In Ourselin, S., Joskowicz, L., Sabuncu, M. R., Unal, G. & Wells, W. (eds.) Medical Image Computing and Computer-Assisted Intervent...

    2016

  16. [24]

    Schütt, K. et al. Schnet: A continuous-filter convo- lutional neural network for modeling quantum inter- actions (2017)

    2017

  17. [25]

    Asymptotic behavior of the ground-state charge density in atoms

    Tal, Y . Asymptotic behavior of the ground-state charge density in atoms. Phys. Rev. A18, 1781– 1783 (1978)

    1978

  18. [26]

    & Biermann, S

    Tomczak, J. & Biermann, S. Effective band struc- ture of correlated materials - the case of vo2. Journal of Physics: Condensed Matter19, 365206 (2007)

    2007

  19. [27]

    & Wagner, L

    Zheng, H. & Wagner, L. K. Computation of the correlated metal-insulator transition in vanadium dioxide from first principles. Phys. Rev. Lett.114, 176401 (2015)

    2015

  20. [28]

    Divergence measures based on the shannon entropy

    Lin, J. Divergence measures based on the shannon entropy. IEEE Transactions on Information Theory 37, 145–151 (1991). URLhttps://api. semanticscholar.org/CorpusID:12121632

    1991

  21. [29]

    Giannozzi, P. et al. Advanced capabilities for materials modelling with quantum espresso. Journal of Physics: Condensed Matter29, 465901 (2017). URLhttps://doi.org/10.1088/ 1361-648X/aa8f79

    2017

  22. [30]

    Giannozzi, P. et al. Quantum espresso: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter21, 395502 (2009). URLhttps://doi.org/10.1088/ 0953-8984/21/39/395502

    2009

  23. [31]

    Kim, J. et al. Qmcpack: an open source ab initio quantum monte carlo package for the electronic structure of atoms, molecules and solids. Journal of Physics: Condensed Matter30, 195901 (2018). URLhttps://doi.org/10. 1088/1361-648X/aab9c3

    2018

  24. [32]

    Kent, P. R. C. et al. Qmcpack: Advances in the development, efficiency, and applica- tion of auxiliary field and real-space varia- 20 tional and diffusion quantum monte carlo. The Journal of Chemical Physics152, 174105 (2020). URLhttps://doi.org/10.1063/ 5.0004860. https://pub...

    2020 doi

  25. [33]

    Krogel, J. T. Nexus: A modular workflow management system for quantum simulation codes. Computer Physics Communications 198, 154–168 (2016). URLhttps://www. sciencedirect.com/science/article/pii/ S0010465515002982

    2016

  26. [34]

    Robust smoothing of gridded data in one and higher dimensions with missing val- ues

    Garcia, D. Robust smoothing of gridded data in one and higher dimensions with missing val- ues. Computational Statistics & Data Analysis 54, 1167–1178 (2010). URLhttps: //www.sciencedirect.com/science/ article/pii/S0167947309003491

    2010

  27. [35]

    A fast all-in-one method for automated post-processing of piv data

    Garcia, D. A fast all-in-one method for automated post-processing of piv data. Experiments in Fluids 50, 1247–1259 (2011)

    2011

  28. [36]

    & Johannes Dolman, A

    Wang, G., Garcia, D., Liu, Y ., de Jeu, R. & Johannes Dolman, A. A three-dimensional gap filling method for large geophysical datasets: Application to global satellite soil moisture ob- servations. Environmental Modelling & Software 30, 139–142 (2012). URLhttps://www. scienced...

    2012

  29. [37]

    Zhang, K. et al. Practical blind image de- noising via swin-conv-unet and data synthe- sis. Machine Intelligence Research20, 822– 836 (2023). URLhttps://doi.org/10.1007/ s11633-023-1466-0

    2023

  30. [38]

    Blaiszik, B. et al. The materials data facility: Data services to advance materials science research.JOM 68, 2045–2052 (2016). Supplementary Information for: Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filter...

    2016

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.