DBNets2.0: Inference for Protoplanetary Discs

• The paper introduces DBNets2.0, a neural simulation-based inference pipeline that jointly estimates planet mass and disc parameters from dust images.
• It compresses high-dimensional images using a CNN into summary statistics and employs an ensemble of normalizing flows to approximate the full joint posterior.
• The method rigorously validates its calibration using synthetic data, exposing parameter degeneracies and enhancing our understanding of planet-disc interactions.

DBNets2.0 is a simulation-based inference pipeline for planet-induced dust substructures in protoplanetary discs. It is designed to infer the full posterior distribution for the planet mass and three additional disc properties—the disc $\alpha$-viscosity, the scale height, and the dust Stokes number—from dust-continuum images, addressing the degeneracy whereby planets of different masses could produce the same rings and gaps if other physical disc properties were different (Ruzza et al., 12 Jun 2025). In formal terms, the target is the joint posterior

$$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$

where $x$ denotes the observed image. The method replaces costly grid-based parameter scans with a two-stage neural estimator that compresses an input disc image into learned summary statistics with a convolutional neural network and then uses an ensemble of normalizing flows to approximate the full joint posterior (Ruzza et al., 12 Jun 2025).

1. Scientific setting and inference target

Protoplanetary discs frequently exhibit concentric rings and gaps in the distribution of millimetre-sized grains. A leading hypothesis is that these substructures trace the gravitational influence of embedded planets: a planet of mass $M_p$ at orbital radius $r_p$ pushes gas away, opening a partial gap whose pressure gradient in turn traps drifting dust (Ruzza et al., 12 Jun 2025). DBNets2.0 is constructed around the observation that inferring $M_p$ in isolation leads to large, model-dependent uncertainties, because the same dust morphology can arise from different combinations of planet mass and disc parameters.

The parameterization adopted by the method is

$$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$

or equivalently $\theta = (M_p,\alpha,h,\mathrm{St})$, depending on whether the planet property is expressed as a mass ratio or as an absolute mass after conversion with the stellar mass. Here $\alpha$ is the Shakura–Sunyaev viscosity parameter, $h=H/R$ is the disk aspect ratio at the planet location, $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$0 is the dust Stokes number, and $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$1 is the planet-to-star mass ratio (Ruzza et al., 13 Mar 2026). The central methodological requirement is therefore not a single best-fit estimate, but a statistically valid posterior that resolves degeneracies between these quantities.

This framing also clarifies a common misconception in the interpretation of disc substructures: dust morphology does not uniquely encode planet mass. DBNets2.0 is explicitly motivated by the need to constrain the full four-parameter space jointly rather than treating gap width or depth as a one-parameter proxy for $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$2 alone.

2. Synthetic data and forward model

The original DBNets2.0 study generates $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$31,300 two-dimensional hydrodynamical simulations of a viscous, locally isothermal gas disc with an embedded planet, using FARGO3D (Ruzza et al., 12 Jun 2025). The key input parameters are drawn via Latin hypercube sampling from

$$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$4

Gas evolution is coupled with a pressureless dust fluid, neglecting back-reaction and self-gravity.

From each density snapshot, the thermal continuum brightness is computed as

$$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$5

where $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$6 is set by vertical hydrostatic equilibrium, fixing $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$7, and $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$8 is a constant opacity. Images are convolved with a range of Gaussian beams, with $$\theta = \bigl(M_p,\ \alpha,\ h,\ \mathrm{St}\bigr), \qquad p(\theta\mid x),$$9, and standardized to $x$0 pixels with zero mean and unit variance (Ruzza et al., 12 Jun 2025). After discarding cases with no clear substructure, the final training and validation set comprises $x$1 images and the test set $x$2.

The exoALMA application describes the same general program in broader operational terms: generate a large training set of synthetic continuum images from 2D hydrodynamical simulations plus simple radiative-transfer post-processing, then learn a neural conditional density estimator $x$3 that approximates the true posterior (Ruzza et al., 13 Mar 2026). In that description, the raw dust-continuum image $x$4 is deprojected to face-on geometry, rescaled so that the hypothesized planet radius $x$5 lies at unit radius, standardized, and then passed through a convolutional summary network.

These choices define the statistical support on which DBNets2.0 operates. A plausible implication is that the method’s posterior validity is tied to the representativeness of this synthetic training distribution, particularly with respect to the single-planet, locally isothermal, and pressureless-dust assumptions.

3. Neural architecture and Bayesian formulation

DBNets2.0 is a two-stage neural estimator. In the first stage, a CNN transforms the high-dimensional image $x$6, together with its beam size $x$7, into 1,500 samples of a 4-vector $x$8; these samples serve as summary statistics for the posterior estimator (Ruzza et al., 12 Jun 2025). During training, each image is randomly translated, rotated, noised with Gaussian $x$9, masked near the outer boundary, and convolved with a random beam $M_p$0, with the chosen beam size passed as a separate scalar input.

The CNN architecture consists of an initial image-augmentation block followed by four Residual Convolutional Blocks, each comprising three 2D convolutions, batch normalization, ELU activations, a skip connection, and then $M_p$1 max-pooling. The resulting features are flattened, concatenated with the beam-embedding dense output, and passed through two $M_p$2 fully connected layers with dropout of $M_p$3. The final activation is $M_p$4, mapping to $M_p$5 and matching the normalized target range (Ruzza et al., 12 Jun 2025). Training minimizes the mean-squared error

$M_p$6

with Adam, using learning rate $M_p$7, batch size $M_p$8, up to 3,000 epochs, and 5-fold cross-validation to prevent overfitting.

At inference time, dropout is enabled to collect 1,500 stochastic forward passes $M_p$9, treated as noisy summaries drawn from the unknown $r_p$0. In the second stage, an ensemble of Masked Autoregressive Flows models the conditional density

$r_p$1

Each flow defines an invertible mapping $r_p$2 to a Gaussian base density, giving

$r_p$3

The flows are trained by minimizing the negative log-likelihood

$r_p$4

using the sbi toolkit and early stopping when validation loss plateaus (Ruzza et al., 12 Jun 2025).

The Bayesian target is

$r_p$5

Because the simulator yields synthetic images $r_p$6 cheaply in batch, DBNets2.0 performs likelihood-free SBI: instead of explicitly computing $r_p$7, it learns the mapping $r_p$8 via neural density estimation (Ruzza et al., 12 Jun 2025). The exoALMA presentation describes this same object as a neural conditional density estimator $r_p$9 that approximates the true posterior and is evaluated on deprojected, standardized local image patches (Ruzza et al., 13 Mar 2026).

4. Validation, calibration, and parameter degeneracies

Validation on synthetic in-distribution tests is based on TARP, the Test of Accuracy with Random Points introduced by Lemos et al. 2023 (Ruzza et al., 12 Jun 2025). For each simulated test case $M_p$0, the method draws a posterior credibility interval of size $M_p$1 around a random point in the support and computes the empirical coverage probability $M_p$2. For a well-calibrated posterior, $M_p$3 for all $M_p$4.

For the 4D joint posterior, the reported Kolmogorov–Smirnov $M_p$5-value between $M_p$6 and the diagonal is 0.999, indicating no bias, and the area-difference “atc” is $M_p$7, close to zero (Ruzza et al., 12 Jun 2025). Marginal 1D credal tests also show unbiased coverage for each parameter. Using the posterior median as point estimate, DBNets2.0 evaluates

$M_p$8

and $M_p$9 over the test set. Planet mass achieves $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$0 in normalized units and $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$1; the other parameters show slightly larger scatter but remain well within the training range (Ruzza et al., 12 Jun 2025).

Posterior samples expose several pairwise degeneracies. The relation between $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$2 and $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$3 shows a strong positive correlation, with $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$4. The relation between $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$5 and $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$6 follows $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$7, matching the analytic scaling in gap-width coefficients

$$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$8

The relation between $$\boldsymbol \theta = \bigl(\alpha,\;h,\;\mathrm{St},\;M_p/M_\star\bigr),$$9 and $\theta = (M_p,\alpha,h,\mathrm{St})$0 follows $\theta = (M_p,\alpha,h,\mathrm{St})$1, comparable to

$\theta = (M_p,\alpha,h,\mathrm{St})$2

These results make explicit that DBNets2.0 is not only a point-estimation tool but a posterior estimator intended to recover the structure of the inference problem itself (Ruzza et al., 12 Jun 2025).

5. Applications to ALMA and exoALMA observations

DBNets2.0 was applied to a set of 49 gaps in 34 protoplanetary discs’ continuum observations, using a heterogeneous collection of ALMA Band 6/7 data for which inclination, position angle, distance, and an assumed planet radius $\theta = (M_p,\alpha,h,\mathrm{St})$3 per gap are known (Ruzza et al., 12 Jun 2025). For each gap, the output is the full joint posterior $\theta = (M_p,\alpha,h,\mathrm{St})$4. The aggregated results show typically low values of $\theta = (M_p,\alpha,h,\mathrm{St})$5-viscosity, disc scale heights, and planet masses. The viscosity is typically $\theta = (M_p,\alpha,h,\mathrm{St})$6, with 57% below $\theta = (M_p,\alpha,h,\mathrm{St})$7 and only a few cases above $\theta = (M_p,\alpha,h,\mathrm{St})$8; the aspect ratio is peaked at $\theta = (M_p,\alpha,h,\mathrm{St})$9 and skewed to lower values; the dust Stokes number has a broad distribution with typical $\alpha$0; and 83% of inferred planets are below $\alpha$1, with median masses per gap typically $\alpha$2 (Ruzza et al., 12 Jun 2025).

These low masses are consistent with the non-detections of putative embedded planets in direct imaging surveys, since the embedded planets are too light and too cold to detect directly at current contrast levels. The inferred viscous timescales are $\alpha$3, corresponding to $\alpha$4 yr at 50 au, and this suggests that angular-momentum removal in these discs may be wind-dominated rather than purely viscous (Ruzza et al., 12 Jun 2025).

The exoALMA XXIII study applies DBNets2.0 to 19 substructures in 13 of the 15 exoALMA disks, assuming that the observed dust morphologies are due to embedded planets at fixed locations (Ruzza et al., 13 Mar 2026). In that workflow, one chooses a substructure location $\alpha$5, extracts the local image patch in the radius range $\alpha$6, deprojects and standardizes it, passes it through the summary CNN, evaluates the normalizing flow to produce $\alpha$7, draws $\alpha$8 samples, converts $\alpha$9 to $h=H/R$0 using stellar masses, and flags estimates with confidence score $h=H/R$1 or posteriors pushed against training priors as uncertain. The exoALMA study reports good agreement in most cases with literature estimates derived with different methods, finds that only three putative planets are expected to migrate outward, and finds no remarkable trend between inferred disk and planet properties and the disks’ gas-to-dust mass ratio, non-axisymmetry index, and masses of the gas, dust, and host stars (Ruzza et al., 13 Mar 2026).

6. Assumptions, limitations, and significance

DBNets2.0 is explicitly conditioned by its training set assumptions. The exoALMA summary states that the training set is limited to single-planet, 2D locally isothermal disks with uniform dust size, no coagulation, and no back-reaction; the planet is held on a fixed orbit; morphological signatures of migration are not modeled; the method assumes axisymmetric substructures; and non-axisymmetric vortices or eccentric gaps may degrade performance (Ruzza et al., 13 Mar 2026). The original DBNets2.0 study likewise specifies a viscous, locally isothermal gas disc, a pressureless dust fluid, and neglect of back-reaction and self-gravity (Ruzza et al., 12 Jun 2025).

These limitations are important for interpreting both successes and nontrivial failure modes. A common misconception is that a posterior over $h=H/R$2 removes model dependence entirely. DBNets2.0 does not remove model dependence; rather, it relocates it into a simulation-based prior over disc physics, image formation, and substructure morphology. This suggests that posterior calibration is rigorous within the support of the training distribution, while extrapolation to migrating planets, multi-planet systems, strongly non-axisymmetric substructures, or broader dust physics is not established by the reported tests.

Within that domain, DBNets2.0 provides a fast, uncertainty-aware mechanism for translating high-resolution dust-continuum images into joint constraints on planet masses and disc physics. The original study reports that the tool is publicly available (Ruzza et al., 12 Jun 2025), and the exoALMA deployment shows how the same framework can be used for a homogeneous population-level analysis of circumstellar disks (Ruzza et al., 13 Mar 2026). In that sense, DBNets2.0 occupies a specific methodological niche: it is a calibrated SBI pipeline for posterior inference on planet–disc parameters from dust morphology, rather than a generic image classifier or a purely empirical gap-scaling prescription.