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The paper argues that molecular design should optimise expectations over the Boltzmann ensemble of conformations, and that the DECAF loop — two coupled flows with an annealing acceptance rule — makes those ensemble statistics the design tar

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2026-08-01 12:29 UTC pith:3M7NMLW2

load-bearing objection DECAF is a genuinely new and promising way to make Boltzmann ensembles the design target, but its headline higher-moment result currently rests on the surrogate it was trained to satisfy; the MD validation is too thin to close the loop. the 3 major comments →

arxiv 2607.19519 v1 pith:3M7NMLW2 submitted 2026-07-21 stat.ML cs.LG

Boltzmann-Expected Molecular Design with Decoupled Annealing Flows

Selma Moqvist , Richard Beckmann , Ross Irwin , Roc\'io Mercado , Simon Olsson This is my paper
classification stat.ML cs.LG
keywords Boltzmann-expected designmolecular designflow matchingdecoupled flowssimulated annealingconformational ensemblesradius of gyrationhigher-moment optimisation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Drug-like molecules do not have one 3D shape; they wander over many conformations, and most properties that matter, such as free energies and shape descriptors, are averages over that wandering. DECAF makes those Boltzmann averages the explicit target of molecular design instead of optimizing a single conformer. It couples two learned conditional flows: one draws ensembles of conformations for a given graph, the other proposes new graphs from conformations. A simulated-annealing acceptance rule scores each proposed graph on statistics of the sampled ensemble, so shifting a distribution's mean, variance, or skewness becomes the optimisation objective. The paper shows that this ensemble-aware loop shifts mean radius of gyration and solvent-accessible surface area toward targets, handles correlated multi-objective trade-offs, and shapes higher moments, with all-atom molecular dynamics used to check the surrogate.

Core claim

The central claim is that 3D molecular design should optimise expectations over the Boltzmann ensemble of conformations, and that the DECAF loop achieves this by factorising p(x,G) into pθ(x|G) — a Boltzmann emulator that samples conformations for a fixed graph — and pθ(G|x), a graph proposer that generates candidate graphs from coordinates. Sampling an ensemble X from the emulator, proposing G′ from each x∈X, and accepting G′ with probability min{1, exp(−τ(f(X′)−f(X)))} makes the ensemble statistic f(X) the design target, and changing objective requires no retraining, only a new scoring function. The experiments claim that on drug-like molecules, ensemble averaging recovers optimisation qua

What carries the argument

The load-bearing machinery is the pair of decoupled conditional flows. pθ(x|G) is a continuous normalising flow trained by conditional flow matching; it acts as a Boltzmann emulator, meaning it need only match the true Boltzmann distribution in expectation over the observables of interest (F-thermodynamic consistency), not pointwise. pθ(G|x) is a discrete flow trained by discrete flow matching; it proposes new graphs conditioned on a slightly perturbed set of coordinates. Alternating the two flows turns a random walk over graphs into a simulated-annealing optimisation: the score f is evaluated on an ensemble drawn from pθ(x|G), and acceptance uses the difference in ensemble scores, so the op

Load-bearing premise

The graph-conditioned flow p(x|G) is trained on static conformers that the authors state are not Boltzmann-distributed, and the paper's Limitations section concedes that its fidelity to the true Boltzmann distribution on the out-of-distribution graphs proposed during optimisation is not guaranteed in general; if this surrogate is wrong for a proposed graph, DECAF may shift surrogate statistics without shifting true Boltzmann ensemble statistics.

What would settle it

Take DECAF-optimised molecules that avoid amide bonds and stereocentres, simulate each with long, converged all-atom MD (or replica-exchange) initiated from multiple conformers, and compare MD-computed mean, variance, and skewness of Rg and SASA against pθ(x|G) estimates. If, for graphs whose conformations stay within the emulator's training-like distribution, MD systematically disagrees with the emulator's ensemble statistics — or if a single-conformer baseline matches MD targets at least as well — the central claim that ensemble-aware optimisation acts on Boltzmann expectations is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Ensemble-aware optimisation shifts mean Rg and SASA toward user targets on drug-like molecules, and moderately sized ensembles (10–50 conformers) recover performance where single-conformer optimisation fails on molecules above roughly 50 atoms.
  • Because the objective is a plug-in scoring function on ensemble statistics, DECAF can switch between minimisation, maximisation, target-value matching, and multi-objective trade-offs with no retraining of either flow.
  • Properties coupled through molecular geometry, such as Rg and SASA, can be traded against each other in all four optimisation directions; the attainable shifts reflect the physical correlation, with joint minimisation easiest and contrasting directions harder.
  • Higher moments of conformational distributions are optimisable: maximising variance and skewness of Rg produces molecules whose MD-simulated distributions are broader and biased toward compact states, a capability not present in single-conformer generative models.
  • Graphs optimised by the ensemble-aware loop keep their ensemble-level property predictions closer to all-atom MD estimates than graphs from single-conformer baselines, especially for in-distribution target values.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A direct testable extension would swap the static-conformer-trained emulator for one trained on long MD or replica-exchange trajectories; the modular loop predicts even closer MD agreement, especially for higher moments and amide-containing molecules.
  • The noisy-MC acceptance rule places DECAF in the pseudo-marginal family: as ensemble size grows the acceptance bias shrinks, so pseudo-marginal MCMC convergence theory could characterise when the walk approximately samples a target distribution over graphs.
  • The same Boltzmann-expected formulation should transfer to observables beyond Rg and SASA — for example solvation or binding free energies — but only once cheap, F-thermodynamically consistent emulators for those observables exist; DECAF's contribution is the optimisation loop, not the surrogate.
  • Because the emulator is reflection-invariant, stereochemistry is not controlled; a stereochemistry-aware emulator or an added penalty term would be needed before using DECAF in chiral environments.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper frames 3D molecular design as the optimisation of molecular graphs for expectations over the Boltzmann ensemble of 3D conformers. It introduces DECAF, which factorises the joint distribution over graphs and coordinates into a graph-conditioned Boltzmann emulator pθ(x|G) and a coordinate-conditioned graph proposer pθ(G|x). These are alternated in a simulated-annealing loop whose acceptance score is computed on ensembles sampled from pθ(x|G), allowing changes of objective without retraining. On GEOM-Drugs, the method is evaluated for shifting mean Rg/SASA, multi-objective trade-offs, target-value optimisation compared with PropMolFlow using MD validation, and higher-moment design (variance and skewness of Rg) with partial MD verification.

Significance. If the results hold, DECAF is a genuinely useful contribution: it explicitly targets ensemble properties rather than single conformers, the decoupled-flow formulation is modular and objective-agnostic, and the multi-objective and higher-moment experiments go beyond existing 3D generative models. The manuscript is unusually candid about limitations (non-Boltzmann training data, heuristic annealing, surrogate fidelity on out-of-distribution graphs, reflection invariance). It also provides independent grounding: Appendix C compares emulator moments with all-atom MD on a 500-molecule test set, and Table 1 reports MD-based MAE for target-value experiments. Those strengths are real. However, the central evaluation is largely carried by the same surrogate used inside the optimisation, and the distinctive higher-moment claim lacks a quantitative success rate from MD.

major comments (3)
  1. [§4.1–4.2, Figs. 2–3; Eq. (4)] The main single- and multi-objective results are evaluated with pθ(x|G), the same surrogate that scores the optimisation in Algorithm 1. Δlocal and Δglobal in Figs. 2–3 are therefore model-internal statistics. The paper acknowledges this in the Limitations section ('optimisation quality is bounded by the accuracy of this surrogate'), but the central claim that DECAF 'produces molecules whose mean Rg/SASA shift toward targets' needs independent confirmation on out-of-distribution graphs. Independent MD validation is provided only for the target-value experiment (Table 1) and for emulator mean agreement on the test set (Appendix C). Please add MD validation for a representative sample of the size-stratified and multi-objective optimisations, or explicitly restrict the claims to surrogate-verified shifts and state which parts remain emulator-internal.
  2. [§4.4, Appendix E.1; Appendix C.1] The higher-moment design is the paper's stated unique contribution, but its MD validation is incomplete. Appendix C, Fig. 9 shows that pθ(x|G) overestimates the variance of Rg relative to 15 ns MD and that skewness histograms disagree, with the disagreement attributed to amide bonds. Appendix E.1 states that all 100 optimised graphs were simulated, yet Fig. 21 displays only 20 'successful examples', no explicit success criterion or pass/fail count is given, and Fig. 22 includes graphs 'not successfully validated due to the discussed limitation'. Without a success rate, the reader cannot tell whether DECAF shapes true Boltzmann variance and skewness or only the emulator's over-dispersed surrogate distribution on favourable cases. Please report the pass/fail count, the criterion used, and separate results for amide-containing and amide-free optimised graphs.
  3. [§4.3, Table 1; Appendix D.1] The PropMolFlow comparison is confounded. In all baseline experiments, DECAF is forced to reject graphs containing amide bonds ('we add a graph constraint to DECAF in all our baseline experiments'), while PropMolFlow is not similarly constrained. Since Appendix C identifies amide-containing molecules as the main source of emulator/MD discrepancy, this constraint likely inflates DECAF's apparent advantage in Table 1. The paper should apply the same constraint to both models, or report the comparison without the constraint and discuss the effect on the conclusion that DECAF 'consistently obtain[s] lower MAE' than PropMolFlow.
minor comments (6)
  1. [§2, Eq. (4)] The term 'F-thermodynamic consistency' is introduced via Eq. (4) but the observable class F is never defined. A one-sentence definition would help the reader understand the scope of the claim.
  2. [Algorithm 1 and Fig. 1] Algorithm 1 samples G_{i+1} before X_i, while the Fig. 1 caption describes sampling X_i first. Align the notation to avoid confusion about the sequencing.
  3. [§4.1] The N=1 baseline is described as 'single-configuration estimates', which conflates the ensemble-size ablation with the stochastic noise of a single-sample score. Clarify that N=1 is a one-sample Monte Carlo estimate, not a 'single conformer' property in the usual generative-model sense.
  4. [Appendix C.1] The text argues that the amide-bond discrepancy is due to slow MD mixing and that the emulator may be correct, but it also uses this argument to justify rejecting amide-containing DECAF graphs in the baseline comparison. Please state in the main text that MD validation of amide-containing optimised graphs is inconclusive by the authors' own analysis.
  5. [§4.4] The hypothesis that 'DECAF does not necessarily require exact moment estimates; rather, estimating the direction of improvement is sufficient' is testable by varying ensemble size N. Adding such an ablation would strengthen the higher-moment section.
  6. [General] No code or data availability statement is included despite detailed hyperparameters in Appendix F. A reproducibility statement would be valuable.

Circularity Check

2 steps flagged

Headline mean-shift and all-100 higher-moment figures are surrogate-internal; MD validation exists for target-value means, but the unique higher-moment verification is incomplete.

specific steps
  1. fitted input called prediction [Section 4, Algorithm 1; Fig. 3 caption; Fig. 4D; Section 6 Limitations]
    "We evaluate each initial and optimised graph based on how well the Boltzmann emulator pθ(x|G) reproduces the target observables fk. ... Observables are computed from pθ(x|G) coordinates ... Both moments are computed on samples from pθ(x|G). ... Still, in our reported results we verify the distributional properties in the observable space aligns with those of the surrogate."

    The quantity being optimised and the quantity reported as success are the same fitted surrogate. Algorithm 1 accepts transitions using f(Xi) with Xi ~ pθ(x|G), and Figs. 2-4 compute the headline shifts (Δlocal, Δglobal, variance, skewness) from pθ(x|G) samples. A run that improves the objective is therefore almost tautologically seen to shift those surrogate statistics; this is an evaluation of the optimiser on its own scoring distribution, not independent evidence about true Boltzmann expectations. The paper's own limitation passage concedes that the reported verification is 'against those of the surrogate', and that fidelity to µG on out-of-distribution graphs 'is not guaranteed'. Independent MD validation is provided for the target-value mean experiments (Table 1) and for test-set means

  2. other [Section 4.4 and Appendix E.1]
    "If the MD samples show agreement with the predicted distribution of pθ(x|G), we consider validation of the optimisation trajectory G1 → Gimax successful. Fig. 21 shows 20 successful examples from this experiment ... including graphs that were not successfully validated due to the discussed limitation."

    The abstract's unique higher-moment claim—'we verify the conformational distributions of these higher-moment designs with all-atom MD simulations'—rests on a validation criterion defined as agreement with the same surrogate pθ(x|G) that was used as the optimisation objective. No success count or explicit pass/fail criterion is reported; only 20 'successful examples' are shown, and the remaining graphs are attributed to the surrogate-vs-MD gap conceded in Section 6. This is not a formal equation-level reduction, but the paper itself flags that the verification is relative to the surrogate, making the higher-moment claim substantially supported by the model's own predictions rather than by independent Boltzmann statistics.

full rationale

The core DECAF derivation—factorising p(x,G) into two conditional flows and scoring graph proposals on ensembles from pθ(x|G)—is internally consistent and not derived from the conclusions. The circularity appears in the evidence chain rather than in the algorithm's definition. The headline demonstrations of mean-Rg and mean-SASA shifts (Figs. 2-3) and the all-100-graph higher-moment shifts (Fig. 4D) are computed from pθ(x|G), the very distribution used inside Algorithm 1's acceptance rule. Thus those plots show that the optimiser can move the surrogate's statistics—the expected consequence of the optimisation loop—rather than independently establishing that true Boltzmann ensemble statistics have moved. The paper candidly states this limitation: 'in our reported results we verify the distributional properties in the observable space aligns with those of the surrogate' and 'fidelity to µG on out-of-distribution graphs is not guaranteed in general.' There is real independent grounding: the emulator is benchmarked against all-atom MD on the GEOM-Drugs test distribution for means (Fig. 8), and the target-value experiments are MD-validated (Table 1). The higher-moment MD validation is incomplete—success is defined as agreement with the surrogate and no pass/fail rate is reported—so the distinctive higher-moment claim is only partially externally supported. No load-bearing self-citation chain was found; author-self citations (Semla architecture, Thermodynamic Interpolation) are background or architectural and do not force the paper's conclusions. Overall score 4: partial circularity in the central empirical demonstration, with sufficient independent MD checks to keep the framework from being merely a restatement of its inputs.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on a surrogate Boltzmann emulator rather than a true Boltzmann sampler, plus a small set of hand-chosen objective weights and normalisation bounds. No new physical entities are introduced: 'Boltzmann-expected design' is a framing and DECAF is an algorithm.

free parameters (4)
  • Observable normalisation bounds f_min, f_max per property = not reported numerically; set by hand
    These bounds define g_k in Eq. 11 and Eq. 12 (Appendix B.3). Clipping at these bounds changes the objective landscape and the achieved Pareto front.
  • Objective weights r_k and energy regularisation weight = e.g., 0.96/0.04 single-objective; 0.45/0.45/0.1 or 0.6/0.3/0.1 multi-objective; 0.64/0.32/0.04 higher-moment
    Hand-chosen in Appendix F.5; these balances determine how strongly each term is pushed and thus the reported shifts.
  • Annealing schedule = tau_1 = 50, tau_imax in {500, 1000}, i_tau = 5
    Selected via ablations in Appendix B.2 and used in all main experiments; changes exploration vs greediness.
  • Augmented Tchebycheff parameter rho = 0.1-0.5 depending on task
    Chosen by ablation in Appendix B.3 (Tables 8-11); changes the trade-off between worst-case and weighted-sum terms.
axioms (5)
  • standard math Flow matching and discrete flow matching correctly transport a tractable prior to the data distribution (Eq. 1 and CFM/DFM background).
    Invoked throughout Section 2 and Appendix A as the training basis for p(x|G) and p(G|x).
  • domain assumption A flow trained on GEOM-Drugs conformers approximates the Boltzmann distribution for design-relevant observables, i.e. Eq. 4 holds approximately.
    Section 4 notes GEOM-Drugs is not Boltzmann-distributed; the paper assumes surrogate expectations match true expectations after MD validation. This is the load-bearing premise of calling p(x|G) a Boltzmann emulator.
  • domain assumption MD simulations with GAFF2 at 300 K provide an adequate reference for true Boltzmann ensemble statistics.
    Appendix F.2 uses GAFF2/OpenMM MD as the ground truth for validation, not the semi-empirical potential used to generate GEOM-Drugs.
  • ad hoc to paper The simulated-annealing loop without detailed balance or ergodic proposals is an acceptable graph-search heuristic.
    Section 6 explicitly concedes that classical SA convergence guarantees do not hold and that the pseudo-marginal acceptance criterion is biased unless Eq. 4 is exact.
  • domain assumption Reflection invariance of the E(3)-equivariant emulator does not materially invalidate optimised property distributions.
    Section 6 and Appendix C.2 state that enantiomers/diastereomers cannot be distinguished, and that MD validation is needed for stereochemistry-sensitive outputs.

pith-pipeline@v1.3.0-alltime-deepseek · 33933 in / 13976 out tokens · 123376 ms · 2026-08-01T12:29:50.935769+00:00 · methodology

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read the original abstract

Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ over the Boltzmann distribution over 3D configurations of a molecular graph. However, existing property-guided generative models tie each property to a single structure, ignoring the underlying ensemble. We recast 3D molecular design as $\textbf{Boltzmann-expected design}$ and realise it with $\textbf{DECAF}$ (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow $p(x\mid\mathcal{G})$, acting as a $\textit{Boltzmann emulator}$, and a coordinate-conditioned flow $p(\mathcal{G}\mid x)$, proposing new graphs from 3D information. By alternating the two flows, DECAF optimises molecular graphs with a simulated-annealing acceptance rule whose scoring function is evaluated on ensembles drawn from $p(x\mid\mathcal{G})$, making ensemble statistics, not single-conformer properties, the design target. The resulting loop requires no retraining to change objectives. On GEOM-Drugs, we show that ensemble-aware optimisation produces graphs whose mean radius of gyration and solvent-accessible surface area consistently shift toward targets, while single-conformer optimisation degrades on larger drug-like molecules where Boltzmann distributions are broadest. DECAF extends to multi-objective trade-offs and, uniquely among 3D generative models, to $\textbf{higher-moment design}$: jointly optimising an ensemble property's variance and skewness to produce flexible molecules biased to a prescribed conformational regime: we verify the conformational distributions of these higher-moment designs with all-atom MD simulations.

Figures

Figures reproduced from arXiv: 2607.19519 by Richard Beckmann, Roc\'io Mercado, Ross Irwin, Selma Moqvist, Simon Olsson.

Figure 1
Figure 1. Figure 1: Overview of DECAF From a graph Gi , we sample an ensemble Xi = {xi,n} N n=1 from the graph-conditioned Boltzmann emulator pθ(x | G). Samples from the ensemble are used to propose Gi+1 through the graph-proposing model pθ(G | x). A new ensemble Xi+1 = {xi+1,n} N n=1, corresponding to Gi+1, is sampled from the Boltzmann emulator pθ(x | G), and the scoring function f is evaluated on both Xi and Xi+1. An annea… view at source ↗
Figure 2
Figure 2. Figure 2: Performance comparison of DECAF against the graph size in number of atoms, for [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Results of joint optimisation of Rg and SASA. Observables are computed from pθ(x | G) coordinates, sampled using the initial graph (G1) and optimised graph (Gimax ). DECAF was run us￾ing an ensemble size N = 25. Each scattered point represents the ensemble averaged observable for one graph. (A) Maximising both Rg and SASA. (B) Maximising Rg while minimising SASA. (C) Minimising Rg while maximising SASA. (D… view at source ↗
Figure 4
Figure 4. Figure 4: Optimisation of variance and skewness of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the flow integration times of [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the flow integration times of [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Analysis of convergence of the MD simulations. [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Correlation between mean estimates from 15 ns molecular dynamics simulations and [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Log-scale histograms of moments estimated from MD samples (15 ns trajectories per [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Log-scale histograms of moments estimated from MD samples (15 ns trajectories per [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Histograms of Rg, evaluated under the Boltzmann emulator pθ(x | G) (blue) and molecular dynamics simulations (orange). We also provide the minimum and maximum Rg structures from the molecular dynamics simulation. (A) The molecular dynamics simulation initiated from the maximum-Rg structure predicted by pθ(x | G). (B) The molecular dynamics simulation initiated from the minimum-Rg structure predicted by pθ… view at source ↗
Figure 12
Figure 12. Figure 12: Histograms of the first 30 dihedral angles of the molecule depicted in Fig. 11, computed [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Histograms of Rg, evaluated under the Boltzmann emulator pθ(x | G) (blue) and molecular dynamics simulations (orange). We also provide the minimum and maximum Rg structures from the molecular dynamics simulation. (A) The molecular dynamics simulation initiated from the maximum-Rg structure predicted by pθ(x | G), compared to the output of DECAF. (B) The molecular dynamics simulation initiated from the min… view at source ↗
Figure 14
Figure 14. Figure 14: Histograms of the first 30 dihedral angles of the molecule depicted in Fig. 13, computed [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Performance comparison of DECAF against the graph size in number of atoms, for [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Performance comparison of DECAF against the graph size in number of atoms, for [PITH_FULL_IMAGE:figures/full_fig_p032_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Performance comparison of DECAF against the ensemble size [PITH_FULL_IMAGE:figures/full_fig_p032_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Performance comparison of DECAF against the ensemble size [PITH_FULL_IMAGE:figures/full_fig_p033_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Performance comparison of DECAF against the ensemble size [PITH_FULL_IMAGE:figures/full_fig_p033_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Performance comparison of DECAF against the ensemble size [PITH_FULL_IMAGE:figures/full_fig_p034_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Comparison of log-scale densities of Rg/atom (Å), computed on coordinates from pθ(x | G) and equilibrium MD samples for 20 successfully optimised graphs [PITH_FULL_IMAGE:figures/full_fig_p035_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Densities of variance and skewness of the optimised graphs, evaluated on molecular [PITH_FULL_IMAGE:figures/full_fig_p036_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: shows the distribution of Rg and SASA values of the initial and optimised distributions across all graph sizes and conformers for the experiments with ensemble size N = 1 in [PITH_FULL_IMAGE:figures/full_fig_p036_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: shows the distribution of Rg and SASA values of the initial and optimised distributions across all graph sizes and conformers for the experiments with ensemble size N = 10 in [PITH_FULL_IMAGE:figures/full_fig_p036_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: shows the distribution of Rg and SASA values of the initial and optimised distributions across all graph sizes and conformers for the experiments with ensemble size N = 50 in [PITH_FULL_IMAGE:figures/full_fig_p037_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Results of joint optimisation of Rg and SASA. Observables are computed from pθ(x | G) coordinates, sampled using the initial graph (G1) and optimised graph (Gimax ). DECAF was run using an ensemble size N = 1. Each scattered point represents the ensemble averaged observable for one graph. (A) Result of maximising both Rg and SASA. (B) Result of maximising Rg while minimising SASA. (C) Result of minimising… view at source ↗
Figure 27
Figure 27. Figure 27: Results of joint optimisation of Rg and SASA. Observables are computed from pθ(x | G) coordinates, sampled using the initial graph (G1) and optimised graph (Gimax ). DECAF was run using an ensemble size N = 10. Each scattered point represents the ensemble averaged observable for one graph. (A) Result of maximising both Rg and SASA. (B) Result of maximising Rg while minimising SASA. (C) Result of minimisin… view at source ↗
Figure 28
Figure 28. Figure 28: Example output structures of DECAF obtained when maximising [PITH_FULL_IMAGE:figures/full_fig_p042_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Example output structures of DECAF obtained when minimising [PITH_FULL_IMAGE:figures/full_fig_p042_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Example output structures of DECAF obtained when maximising SASA. [PITH_FULL_IMAGE:figures/full_fig_p043_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Example output structures of DECAF obtained when minimising SASA. [PITH_FULL_IMAGE:figures/full_fig_p043_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Example output structures of DECAF obtained when jointly maximising [PITH_FULL_IMAGE:figures/full_fig_p044_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Example output structures of DECAF obtained jointly minimising [PITH_FULL_IMAGE:figures/full_fig_p044_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: Example output structures of DECAF obtained when jointly maximising [PITH_FULL_IMAGE:figures/full_fig_p045_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Example output structures of DECAF obtained when jointly minimising [PITH_FULL_IMAGE:figures/full_fig_p045_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Example output graphs of DECAF obtained when maximising variance and maximising [PITH_FULL_IMAGE:figures/full_fig_p046_36.png] view at source ↗

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