Title: Inductive Domain Transfer In Misspecified Simulation-Based Inference
Venue: NeurIPS 2025
Accepted: yes
Keywords: AI4Science

SBI

Domain transfer

sim2real
Abstract: Simulation-based inference (SBI) of latent parameters in physical systems is often hindered by model misspecification--the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, a recent SBI approach, addresses this challenge through a two-stage domain transfer process that combines semi-supervised calibration with optimal transport (OT)-based distribution alignment. However, RoPE operates in a fully transductive setting, requiring access to a batch of test samples at inference time, which limits scalability and generalization.  We propose a fully inductive and amortized SBI framework that integrates calibration and distributional alignment into a single, end-to-end trainable model. Our method leverages mini-batch OT with a closed-form coupling to align real and simulated observations that correspond to the same latent parameters, using both paired calibration data and unpaired samples. A conditional normalizing flow is then trained to approximate the OT-induced posterior, enabling efficient inference without simulation access at test time. 
Across a range of synthetic and real-world benchmarks--including complex medical biomarker estimation--our approach matches or exceeds the performance of RoPE, while offering improved scalability and applicability in challenging, misspecified environments.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a method for addressing misspecification in SBI. The method builds on RoPE, a recently published method that addresses the same challenge, and eliminates RoPE's need for a calibration set of real observations during inference. This is achieved by 1.) incorporating the callibration set into the fine-tuning objective of the pretrained NPE embedding network, and 2.) by adapting the optimal transport objective to allow for inductive inference requiring only a single observation. Finally, the authors propose to train an additional normalizing flow to amortize the computation of the inference-time OT plan.\nThe authors evaluate their method in comparison to RoPE and various ablations mainly using the tasks, metrics, and experiments considered in the RoPE paper.\n\nSTRENGTHS AND WEAKNESSES:\nThis paper tackles the important challenge of handling simulator misspecification in SBI. \n\n## Strengths\n- The method addresses some proper limitations of RoPE, particularly its dependence on a calibration set of real observations during inference.\n- The authors consider many ablations and include an experiment concerning label noise robustness. This is highly relevant in the RoPE setting, where access to pairs of real observations and ground truth parameter measurements (which might be noisy) is assumed.\n\n## Weaknesses\n\n### OT with $\\rho = 0$:\nTo make their method inductive rather than transductive, the authors drop the column-marginal constraint of the semi-balanced OT objective used in RoPE. This enables them to obtain a closed-form transport plan that does not depend on other observations. In particular, they write:\n> While being more computationally intensive for training, such approaches are also known for leading to biased OT solutions and a significant sensitivity to the chosen batch size, hence further motivate our choice for $\\rho = 0$.\n\nHowever, the claim about biased OT solutions and the general OT framing is slightly baffling, as completely dropping the column-marginal constraint (which is $\\rho=\\infty$ for balanced OT) results in something that basically ceases to be optimal transport?\nRather, the \"transport plan\" the authors obtain with $\\rho = 0$ is a normalized squared exponential kernel that weights certain simulations higher than others based on the distance between their embedding and the observation's embedding. \n\nThis might be a reasonable thing to do, but the authors should more clearly describe that this is what they do, and explain why this might be a reasonable thing to do.\n\n### Finetuning objective:\nThe $\\rho =0$ transport plan is also used in the finetuning objective, combined with the supervised loss used in RoPE. However, it's unclear what the exact role of the OT part in the objective is. The authors write:\n> In contrast, when calibration pairs are noisy or mismatched, the two objectives may conflict, allowing the term to compensate for uncertainties in the calibration set.\n\nThe paper does not discuss how this compensation works, especially given the special transport plan.\n\n### Complexity and hyperparameter tuning:\nWhile the authors mention this limitation, the method includes quite a few complex steps, which hinders applicability. \nUsers need to first train an NPE flow and an embedding net. Then, the finetuning of the embedding net is based on a modified objective, which introduces another hyperparameter $\\lambda$ (beyond the hyperparameter for the entropy regularization $\\gamma$).\nFinetuning is followed by training another flow to amortize over the computation of the transport plan.\n\nThe discussion of how to choose these hyperparameters, particularly $\\lambda$, and their effect on inference is insufficient.\nFurthermore the method still assumes access to two different calibration sets. \n\n### Experiments:\nWhile the authors consider many different ablations, the paper does not consider all the tasks performed in RoPE.\n\nQUESTIONS:\n- Can the authors provide some mathematical justification why the $\\rho=0$ transport plan is a good choice, and what posterior one obtains in the end? Does the self-calibration property of RoPE or something similar still hold when $\\rho=0$?\n- How should users tune $\\lambda$?\n- Have the authors considered different types of regularization other than the OT term in Eq. (4)? Replacing or dropping it would eliminate the dependence on the callibration set of observations during finetuning. How exactly does the OT term compensate, if the supervised term is off?\n- Since their paper is so closely related to RoPE, could the authors also apply their method to the CS and SIR task? Or was there a good reason not to?\n- Some numbers that should be consistent between this paper and the RoPE paper seem different? Why is that? E.g. the LPP for the SBI upper bound on the light tunnel task.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper deals with the issue of misspecification in amortized simulation-based inference (SBI).\nSpecifically, in amortized SBI such as neural posterior estimation (NPE) one would train a neural network and possibly a neural statistics encoder such that given a dataset $x$ and encoded dataset $h(x)$ --> the network learns to map to the posterior $q(\\theta| h(x))$.\nThe issue is that $h(x)$ and $q(\\cdot)$ are trained using synthetic data (via a simulator). The real generative process may deviate from the simulator, leading to model misspecification / covariate shift.\n\nPrevious work (RoPE) addressed the issue via optimal transport, but had strong requirements (e.g., requiring a batch of test samples for inference). This work addresses multiple limitations of RoPE, including provided an amortized posterior estimation method based on optimal transport. The paper first introduces the method for joint supervised & OT training, and then how to amortize it.\n\nThe technique is evaluated on four benchmarks, with additional ablation studies and an analysis of robustness to noise.\n\nSTRENGTHS AND WEAKNESSES:\nOverall, this is a solid paper tackling a very timely and significant issue, which is robustness of amortized SBI techniques to model misspecification (also known as *sim2real gap*). The approach is original and using state-of-the-art techniques, such as optimal transport (OT). The paper is generally well written and clear.\n\nOne potential weakness of the paper is that all considered baselines focus on OT approaches which require a \"calibration dataset\" (except for the NPE baseline) which consists of real data samples together with their true parameters. Obtaining such data for some applications may be a strong or costly requirement. \nGiven this additional constraint, it'd be useful for the practitioners to see how the proposed method compares to *robust* SBI techniques (beyond vanilla approaches) that do not require real data for calibration (see e.g. Huang et al., \"Learning Robust Statistics for Simulation-based Inference under Model Misspecification\", 2023). I would expect the paper's method to be better, since it leverages this additional information from the calibration set, but it'd be good to indeed see that this is the case.\n\nAs a minor exposition point, I recommend to state clearly the dimensions involved in each problem; that is parameter dimensionality (I think it's 2-4-1-4 or similar) and the dimensionality of the summary statistics. Relatedly, it'd be useful to know to which dimension (of parameters and data) is the method expected to scale.\n\nQUESTIONS:\nPlease see above for my open comments and related questions.\nI'd be happy to increase my score if the authors address my points.\n\nLIMITATIONS:\nThe paper could be more upfront about its limitations -- naturally it inherits limitations of NPE, but it should be added which additional limitations are brought in by the specific methodology.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes an inductive and amortized method in the context of simulation based inference (SBI). Recent published works on SBI, RoPE operate in a transductive setting which uses optimal transport to align simulations to real data, but this needs recomputing the transport equation every for every inference time, which is a major limitation. This paper overcomes this limitation by using a joint training framework for the simulations and real data and an amortised posterior estimation. Experiments on a set of simulated and real world benchmarks provide evidence for the viability of this method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n1) The paper is clearly written and most of the components going into the framework are explained reasonably well. Figures are clear as well.\n2) Addresses an important problem of simulator misspecification in SBI. This is important to sim to real problems in general.\n3) Clear motivation for improving over RoPE’s transductive limitations.\n4) This method could be practically useful since it avoids simulation access at test time which is neat. \n6) The paper provides useful ablation studies to show the importance of the joint training and amortization components.\n\nWeaknesses: \n1) An intuitive explanation of optimal transport is not provided in the main text. This can make it somewhat hard to understand for the readers.\n2) The method seems to be suspectible to noise in the calibration set, which can potentially limit its applicability in a wide range of real world problems where calibration sets are scarce and noisy.\n3) The paper uses mini-batch OT with a fixed entropy regularization parameter gamma, but does not explore how sensitive results are to this value.\n4) The method is evaluated only on problems with up to four parameters. SBI applications often involve ten or more parameters. It is unclear how the OT coupling or the normalizing flow posterior will scale in such regimes, or whether performance degrades under the curse of dimensionality.\n\nQUESTIONS:\nI mainly want some clarifications and some questions: \n\n1) To make sure I understand correctly: the supervised calibration loss is mainly useful when the calibration pairs are accurate, while the OT loss provides robustness when those pairs are noisy or mismatched. Is that correct?\n2) The evaluation datasets have only up to a maximum of four parameters. Oftentimes, complex simulations have a much larger parameter space in fields where SBIs are frequently used, such as complex fluids or astrophysics datasets. Can the authors describe how they expect their model to perform when the parameter dimensionality is very high?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an inductive and amortized framework for simulation-based inference\n(SBI) under model misspecification, building upon the recent RoPE method. The key\ninnovation is combining optimal transport (OT)-based distribution alignment with\nsupervised calibration in a joint training objective, followed by amortization through a\nconditional normalizing flow. This enables single-sample inference without requiring\nsimulations at test time, addressing RoPE's transductive limitations. The method is\nevaluated on synthetic and real-world benchmarks, showing competitive or superior\nperformance to RoPE while offering practical deployment advantages.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n**Quality:**\n\n- Strong technical contribution that addresses real limitations of existing methods\n- Thorough experimental evaluation including ablations to understand component\n  contributions\n- Competitive results across benchmarks while being more practically deployable\n- Clear acknowledgment of method limitations (e.g., reduced confidence with larger\n  calibration sets)\n\n**Clarity:**\n\n- Clear problem motivation and terminology for misspecified SBI scenarios\n- Good concise explanation of the baseline RoPE method\n- Well-structured training procedure box that clarifies the algorithm\n- Appropriate use of same benchmarks as RoPE for direct comparison\n\n**Significance:**\n\n- Addresses important practical limitations of RoPE (transductive nature, need for\n  test-time simulations)\n- Enables deployment of misspecified SBI methods in real-world scenarios requiring\n  single-sample inference\n- Demonstrates effectiveness even with small training sets (1000 samples)\n\n**Originality:**\n\n- Novel combination of joint OT-supervised training with closed-form solutions\n- Creative use of conditional normalizing flows to amortize OT-based posteriors\n- Principled approach to making transductive methods inductive\n\n### Weaknesses\n\n**Clarity:**\n\n- **Section 2.2 (lines 83-97)**: The entropic OT formulation introduces the mathematical\n  framework quite directly, which may be challenging for readers less familiar with\n  optimal transport. Consider adding a brief intuitive explanation before Equation 1,\n  perhaps describing how OT finds correspondences between real and simulated\n  observations in the embedding space to handle the domain shift.\n\n- **Section 3.2**: The amortization step involves a (for me, see question below) subtle\n  but elegant insight that could benefit from additional explanation. When sampling\n  \\theta^{(j,k)} \\sim q\\_{\\psi^*}(\\theta|h\\_{\\omega^*}(x_s^j)), it may not be\n  immediately clear to readers why these parameters sampled from simulation-conditioned\n  posteriors serve as valid training targets for real observations. It might help to\n  explicitly describe the transitive relationship: since $\\theta$ generates $x_s^j$, and\n  $x_s^j$ is matched to $x_r^i$ through OT weights, these $\\theta$ values are also\n  plausible for $x_r^i$.\n\n- **Figure 1**: While the figure shows the two-stage process, the visual flow and\n  notation could be clearer. For instance, $\\rho_f$ is not defined in the caption, and\n  the complex relationships in the cNF training are understandably difficult to capture\n  visually. Perhaps simplifying the notation or adding a legend for the different\n  symbols and arrow types could help readers navigate the diagram.\n\n- **Dataset notation**: The various datasets used throughout the paper\n ($D_{calib}$, $D_u$, $D_{OT}$, $D_{test}$)\n  serve different purposes that may not be immediately clear on first reading. A brief\n  table or list before the Training Procedure box summarizing what each dataset contains\n  and its role in the method could improve clarity - though the Training Procedure box\n  itself is already quite helpful in this regard.\n\n**Quality:**\n\n- **Scalability analysis**: The experiments focus on relatively low-dimensional\n  parameter spaces (≤4D). While these benchmarks allow direct comparison with RoPE, it\n  would be valuable to include some discussion of how the method might scale to higher\n  dimensions, or to explicitly acknowledge this as an area for future investigation.\n\n- **LPP metric details**: Following Lueckmann et al. 2021's recommendations, it would be\n  helpful to specify the number of samples used to compute the LPP metric, as this can\n  affect the reliability of the estimates.\n\n- **Hemodynamics calibration data**: The paper mentions thermodilution for obtaining\n  ground truth cardiac output values (line 179), but additional details about how these\n  measurements correspond to the ABP segments would help readers understand the data\n  collection process and implications w.r.t the limitations in other SBI use cases.\n\n**Significance:**\n\n- **Calibration data requirement**: While the need for paired data with known $\\theta$\n  is inherent to the problem setting, this requirement could be stated more prominently\n  in the introduction (similar to the RoPE paper). This would help readers immediately\n  understand that this approach targets a specific subset of SBI problems where some\n  ground truth is available.\n\n- **Incremental nature**: The contribution builds naturally on RoPE by adding\n  amortization, which is a logical and useful extension. While incremental, it addresses\n  genuine practical limitations that would prevent RoPE's deployment in many real-world\n  scenarios.\n\nQUESTIONS:\n1. In Section 3.2, am I correct in understanding that the conditional normalizing flow\n   learns an implicit mapping from real observations to parameters through the following\n   transitive relationship: (a) \\theta^{(j,k)} \\sim\n   q_{\\psi^*}(\\theta|h_{\\omega}(x_s^j)) gives parameters that likely generated\n   simulation $x_s^j$, (b) High $\\alpha_{ij}$ indicates that real observation $x_r^i$ is\n   similar to simulation $x_s^j$ in embedding space, (c) The flow $q_\\xi$ thus learns\n   that if $x_r^i \\approx x_s^j$ (high $\\alpha_{ij})$, then parameters that generated\n   $x_s^j$ are also likely for $x_r^i$?\n\n2. For the real hemodynamics data, how is the calibration dataset obtained? How are real\n   $\\theta$ values measured in practice?\n\n3. How many samples were used to compute the LPP metric? This is important to avoid bias\n   as noted in Lueckmann et al. 2021.\n\n4. How does the method scale to higher-dimensional parameter spaces? The current\n   evaluation is limited to relatively low-dimensional problems.\n\n5. Have you explored approaches to mitigate the reduced posterior confidence (ACAUC < 0)\n   observed with larger calibration sets?\n\nLIMITATIONS:\nThe authors provide a thoughtful discussion of computational limitations in the\nconclusion. To further strengthen the paper, consider also highlighting earlier in the\nmanuscript:\n\n- The requirement for calibration data with true parameters, which distinguishes this\n  setting from standard SBI where only observations are available\n- Potential scalability considerations for high-dimensional parameter spaces\n- The observed trade-off between calibration set size and posterior confidence\n\nThese clarifications would help readers better understand when this approach is most\napplicable.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-04"}