Title: MaNGO — Adaptable Graph Network Simulators via Meta-Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph Network Simulators

Meta Learning

Graph Neural Operators

Conditional Neural Processes
Abstract: Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven approaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require labor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share a common underlying latent structure.
    In this work, we address these challenges by learning this shared structure through meta-learning, enabling fast adaptation to new physical parameters without retraining. 
    To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To mitigate error accumulation over time, we combine CNPs with a novel neural operator architecture. 
    We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy on unseen material properties close to that of an oracle model.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\n__I have reviewed this paper for ICML. As far as I can tell, the only change to the paper is the title. I will hence re-post my review from ICML.__\n\nThe paper introduces a new GNN-based method for learning physical dynamics. It specifically focusses on latent parameter estimation. Given a set of reference simulations, an encoder create a latent embedding r, which contains an estimate of hidden simulation parameters. A GNN decoder can then use r to perform inference with those material parameters.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper claims better performance on physical simulation by a) a new GNN architecture and b) meta-learned latent parameters (CNP). The claims are supported by experiments, although experimental validation could be improved.\n\nThe method is quite complex, with many choice different to previous work, and it's not immediately obvious to me if they are actually needed or effective.\n- A lot of the complexity comes from CNP, i.e. inferring a latent representation of the hidden material parameters. But then, 3.2. introduces a direct regression loss against the true latent parameters. But if rho has to be assumed known in training, there are much simpler options which need to be tested. The most obvious is training an encoder from D_L -> rho, and conditioning the decoder on rho instead of r. This is much simpler: no Gaussian distribution needed, no potential issues with irrelevant information contaminating the latent. Plus encoder and decoder can be trained separately, severely reducing memory and training time. I would imagine this would actually perform quite well for the datasets investigated in this paper, given the strong performance of the oracle models. (there may be some downsides for ambiguous real-world data, but that's not studied here)\n- The architecture of the encoder is also a bit surprising to me. For (traditional) estimation of material parameters, you'd need spatial and temporal derivatives. Deep sets without any neighborhood information will struggle computing spatial gradients; something like 1 or 2 message passing steps with a short temporal window, and then aggressive spatiotemporal pooling seems like a more obvious choice.\n- EGNO works because the temporal convolution is in Fourier space, i.e. a global operation. Replacing this with a 1D CNN means information will only travel locally, which will likely limit the ability to model long sequences or sequences with complex dynamics (all examples are quite short and contain simple motion).\n\nThere are a lot of novel surprising choices in the model. These need to be properly ablated, and compared to simpler choices (see e.g. the points mentioned under Methods And Evaluation Criteria). I feel the paper tries to do too much, without spending the time to properly evaluate all of its contributions, and we don't end up learned all that much in the end.\n\nFor example, there's actually an interesting point in the core GNN architecture of MGN vs MGNO vs EGNO. EGNO isn't quite made for the type of system studied here, but there may be advantages of this style of approach compared to autoregressive MGN. But this needs to be properly studied, with detailed analysis on pros and cons (e.g. ingesting entire trajectories quite obviously comes with much higher memory footprint, and it's probably not a coincidence that the systems studied here are extremely low-dimensional), ablations to figure out the best configuration for different system types and sizes, etc. There might be good tradeoffs to be had, but this really needs to be its own paper.\n\nSimilarly, material parameter estimation is an important topic for using learned simulator in real-world settings. For this topic, the focus really should be on how to best design an encoder, how to deal with uncertainty (and when that is/isn't important), latent vs. explicit parameter estimation, etc. And most importantly, parameter estimation is fundamentally about real world data (for simulations we can just assume parameters are available). So studying real-world data, or at least a good proxy (where training and testing material model/parameters have a gap) is probably a good idea.\n\nQUESTIONS:\n(my questions were already answered in the last review process)\n\nLIMITATIONS:\nyes, except for what is mentioned above.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces MaNGO, a meta-learning framework for graph-based physics simulators. The goal is to enable fast adaptation to new, unseen physical parameters (e.g., material properties) without retraining. MaNGO uses Conditional Neural Processes (CNPs) to infer a latent representation of these parameters from a few \"context\" examples. This representation then conditions a novel, non-autoregressive decoder—which combines Message Passing Networks (MPNs) for spatial dynamics and a 1D CNN for temporal dynamics—to predict the full simulation trajectory.\n\nSTRENGTHS AND WEAKNESSES:\nStrength\n1.Important Problem: The paper tackles the critical and practical problem of simulator adaptation, which is a major bottleneck in data-driven science and engineering.\n2.Innovative Decoder Design: The non-autoregressive decoder, blending the strengths of MPNs and 1D CNNs, is a smart solution that effectively avoids common issues like error accumulation (from autoregression) and over-constraining (from strict equivariance).\n3.Clarity and Organization: The paper is well-written and logically structured. The motivation, methodology are presented clearly, making the paper easy to follow. \nWeakness\n1.Missing Comparison with Autoregressive Models: The paper claims its non-autoregressive decoder is more memory-intensive but faster than autoregressive ones. However, it lacks a direct experimental comparison with an autoregressive baseline (like a meta-learning version of MGN) to substantiate this trade-off..\n2.Limited Meta-Learning Baselines: The superiority of the proposed CNP-based framework is not fully established, as it is not compared against other prominent meta-learning approaches, such as optimization-based methods like MAML.\n3.The encoder uses a Deep Set to aggregate context features. This might be an oversimplified approach, and the paper does not explore or justify this choice over potentially more sophisticated aggregation methods.\n\nQUESTIONS:\n1.The paper notes that the neural operator framework is more memory-intensive than autoregressive methods. Could you elaborate on the memory complexity and scalability of the non-autoregressive MaNGO decoder, particularly when dealing with long time-series and large-scale graphs ?\n2.Is there a practical limit or \"tipping point\" where MaNGO's memory consumption becomes a significant drawback compared to autoregressive models?\n3.The Deep Set encoder aggregate features from samples into a latent representation. Have you explored alternative, potentially more expressive, aggregation mechanisms?  Was there a comparative study to justify the choice of Deep Sets?\n4.Could you please elaborate on the experimental setup for data partitioning? Specifically, how were the tasks divided into meta-training and meta-test sets? Whether to test samples that have never been seen before during the test？\n\nLIMITATIONS:\nno,I think some comparative experiments should be added.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces Meta Neural Graph Operator (MaNGO), a meta-learned graph–network simulator that i) encodes a set of short \"context\" roll-outs with a spatio-temporal Conditional Neural Process (CNP) encoder, producing a latent code $r$ that captures hidden physical parameters, and ii) decodes an entire future trajectory in a single shot via a new neural-operator-style architecture that alternates spatial message passing and 1-D temporal convolutions. Experiments on four synthetic dynamics datasets show that with as few as 2-3 context simulations MaNGO achieves rollout MSE close to an oracle that knows the ground-truth material constants at test time.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n- **Thorough Experiments (Quality and Significance):** The authors compare against non-meta and oracle baselines, vary the number of context runs, test robustness to noise and drop-out, and explain why ENGO, a strong equivariant baseline, fails on the Planar Bending dataset. This makes the empirical case convincing.\n\n- **Clarity:** The paper is well-written and easy to follow. \n\n- **Well-motivated Problem (Significance):** The paper tackles an important problem: how to make learned simulators handle new material or boundary settings without retraining (which can be computationally very costly).\n\n- **Fresh Meta-learning Angle (Originality):** Treating the task as a Conditional Neural Process (CNP) lets the model learn from just a handful of \"context” simulations, and even predict the hidden physical parameters at the same time.\n\n- **Practical Decoder Design (Originality):** The new decoder removes the heavy SE(3)-equivariant layers equivariant layers, and replaces them with message passing networks and equivariant convolutions with a 1D CNN. It still predicts the entire trajectory in one shot and consistently outperforms the previous baselines on the reported benchmarks.\n\n\n**Weaknesses**\n\n- **Clarity:** This is minor but I believe \"Figure 5\" in line 290 should actually be \"Figure 6\". \n\n- **All synthetic data (Quality, Significance):** Every benchmark comes from a simulator, uses a fixed graph, and has at most $\\approx$ 500 nodes. There is no evidence the method works on larger meshes, changing topologies, or real sensor measurements.\n\n- **High Training Cost (Significance):** Roughly 8,500 GPU-hours for training plus 6,000 GPU-hours for hyper-parameter search is heavy for four mid-scale tasks, and there is no comparison to optimization-based meta-learners like MAML.\n\n- **Fixed Edge Set Assumption (Significance):** The model requires the same graph connectivity across time and tasks, limiting use in problems with fracture, contact loss, or remeshing.\n\nQUESTIONS:\n1) Could you report concrete numbers for MaNGO’s inference‐time GPU memory, and wall-clock latency on the Sphere Cloth Coupling (SCC) benchmark, and compare it with MGN?\n2) Do you have preliminary results on larger (>10 k node) or variable-topology meshes, e.g., fracture or contact-break scenarios? What modifications, if any, would MaNGO require in those settings?\n3) What is the quantitative error (e.g., RMSE) of the regressor $f_\\psi(r)$ when recovering hidden material parameters such as Young’s modulus and Poisson’s ratio on held-out tasks?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
The paper introduces a meta-learning framework that enables Graph Network Simulators to easily adapt to unseen physical parameters without requiring retraining or explicit parameter input at test time. By leveraging Conditional Neural Processes, the proposed method encodes a small set of observed simulations into a latent representation that captures the underlying material behavior. MaNGO outperforms existing GNS baselines across several physics simulation benchmarks, achieving performance close to models with access to simulation parameters.

STRENGTHS AND WEAKNESSES:
## Strengths

- Well written paper that provides detailed theoretical analysis of the task and the method. The figures were also very helpful.

- The authors propose a novel method for critical scenarios where simulation parameters are unknown or unavailable at test time.


- The experimental section is quite rich, demonstrating consistently great results and clearly proving  architectural improvements.

- The method showcases strong generalization to unseen parameters, achieving near-oracle accuracy.


## Weaknesses

- Compared to autoregressive methods, neural operator methods might be more memory-intensive.

QUESTIONS:
- Could the authors provide some insights and comparisons regarding the number of parameters and runtimes?

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 4
IMPACT: 4
ORIGINALITY: 3
DATE: 2025-07-03