Title: Integrating GNN and Neural ODEs for Estimating Non-Reciprocal Two-Body Interactions in Mixed-Species Collective Motion
Venue: NeurIPS 2024
Accepted: yes
Keywords: Deep Learning

Neural Differential Equations

Graph Neural Networks

System Identification

Active Matter

Collective Motion

Non-Reciprocal
Abstract: Analyzing the motion of multiple biological agents, be it cells or individual animals, is pivotal for the understanding of complex collective behaviors. 
With the advent of advanced microscopy, detailed images of complex tissue formations involving multiple cell types have become more accessible in recent years. However, deciphering the underlying rules that govern cell movements is far from trivial. Here, we present a novel deep learning framework for estimating the underlying equations of motion from observed trajectories, a pivotal step in decoding such complex dynamics. 
Our framework integrates graph neural networks with neural differential equations, enabling effective prediction of two-body interactions based on the states of the interacting entities. We demonstrate the efficacy of our approach through two numerical experiments. First, we used simulated data from a toy model to tune the hyperparameters. Based on the obtained hyperparameters, we then applied this approach to a more complex model with non-reciprocal forces that mimic the collective dynamics of the cells of slime molds. Our results show that the proposed method can accurately estimate the functional forms of two-body interactions -- even when they are nonreciprocal -- thereby precisely replicating both individual and collective behaviors within these systems.


Peer reviews:
comments: SUMMARY:
This work proposes a graph neural network-based deep learning model for two-body interactions, which has better efficiency based on two numerical experiments.

STRENGTHS:
Two-body interactions are not my research field. Thus, I don't have enough expertise to evaluate this work. I sent an email to AC to re-assign this paper when I received the assignment. Unfortunately, I didn't receive any feedback. My justification is just based on the writing without any methodology consideration.

WEAKNESSES:
see strengths

QUESTIONS:
see strengths

LIMITATIONS:
see strengths
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-11

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a model combining GNN and Neural ODEs for the task of two-body interaction prediction. Two numerical experiments were conducted to evaluate the model's performance.\n\nSTRENGTHS:\n- Using a GNN and Neural ODE to describe the dynamics of two-body interaction state changes is well-motivated and reasonable.\n- Experiments from interaction models are implemented from simple to complex setups, showing the efficiency and capacity of the proposed method.\n- The paper structure and writing is clear and easy to follow.\n\nWEAKNESSES:\nOne of the main contribution claimed in this paper (as well as in its title) is the combination of GNN and Neural ODE, but this approach has been studied in multiple works back since 2020, the authors seem to overlook the important and related body of works [1,2,3,4]. [2] is a direct competing method (GDE) where the authors proposed a model integrating graph NN and Neural ODEs. GDE-related applications exist as well, for example, social network embedding [5], action recognition [6]. \n\nGiven the missing discussion of related work, and my concern about the major technical contribution claim in this paper, I do not see much merits of this study to be novel and interesting to the community.\n\n[1] L. Xhonneux et al.: Continuous Graph Neural Networks. PMLR 2020.\n[2] M. Poli et al.: Graph Neural Ordinary Differential Equations. AAAI 2020.\n[3] L. Chen et al.: Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-Time Dynamics. AAAI 2024.\n[4] A. Han et al.: From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond. TMLR 2024.\n[5] Y. Zhang et al.: Improving Social Network Embedding via New Second-Order Continuous Graph Neural Networks. KDD 2022.\n[6] L. Pan et al.: Spatial-temporal graph neural ODE networks for skeleton-based action recognition. Scientific Reports 2024.\n\nQUESTIONS:\nThe author should discuss in their response regarding the missing related works that involve integrating GNN+Neural ODEs, and highlight their differences/contribution from previous work.\n\nLIMITATIONS:\nLimitations were discussed in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel deep learning framework for estimating two-body interactions in mixed-species collective motion. The authors combine graph neural networks (GNNs) with neural ordinary differential equations (Neural ODEs) to predict interactions between pairs of entities based on their states. This approach represents the system as a dynamic graph, using GNNs to efficiently calculate interactions and Neural ODEs to learn system dynamics. Authors demonstrate their method via two experiments: a simple harmonic interaction model and a more complex model simulating cellular slime molds. The framework successfully estimates interaction functions and replicates both individual and collective behaviors in these systems. The authors provide detailed quantitative analyses of estimation accuracy and demonstrate the method’s ability to generalize to single-species scenarios after training on mixed-species data.\n\nSTRENGTHS:\nStrengths:\n- Novel integration of GNNs and Neural ODEs for collective motion analysis\n- Ability to handle mixed-species systems and estimate species-dependent interactions (and demonstrating its effectiveness across simple and complex models)\n- Successful generalization to single-species scenarios after training on mixed-species data\n- Potential applicability to a wide range of biological systems exhibiting collective motion\n\nWEAKNESSES:\nWeaknesses:\n- High computational cost and long training times .\n- Current limitation to deterministic motion equations and pairwise interactions.\n- Lack of ablative studies on hyper parameter optimizations and method’s sensitivity to noise.\n- Lack comparative analysis with existing methods for estimating collective motion dynamics.\n\nQUESTIONS:\nQuestions for the authors:\n1. How does the performance of your method compare to existing approaches for estimating collective motion dynamics, such as SINDy or Bayesian optimization methods?\n2. Have you explored the method’s sensitivity to noise in the input data? How robust is the estimation process to measurement errors or stochastic fluctuations in the trajectories?\n3. I’m intrigued by the use of LAMB optimizer. What specific characteristics of your problem or empirical results led you to choose LAMB over AdamW?\n4. What are the primary factors limiting the scalability of your approach to systems with stochastic motion equations and higher-order interactions?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper seeks to model dynamic interactions of biological agents (primarily cellular slimes) by adapting the (continuous time) Langevin model, which models the collective motion of the system from considering individual force terms and the summation of pairwise interactions. Such pairwise interactions can be modelled as a graph; thus the others model the interaction terms with message passing on a graph and the solution to the differential equations are modelled with a neural ODE. The main contribution seems to be the learning of the force terms with fully connected neural networks. The authors claim that the main problem with previous works is that no models have been proposed that can model systems that interact in unknown ways; however, the system is trained in a supervised way based on known simulations. The results suggest the learning model can replicate the simulation,  I don’t believe there was any attempt to extrapolate beyond the training regime.\n\nSTRENGTHS:\n1. The paper describes a very interesting problem which (to my knowledge) hasn’t been extensively explored through learning based approaches\n2. It uses state-of-the-art message passing gnns and Neural ODEs as part of the \n3. The model is accurately replicating simulation behaviour\n4. Code is available\n\nWEAKNESSES:\n1. The paper is really hard to read. It took me a very long time to understand how it was implemented and although the code was generously submitted, this isn’t commented making it difficult to follow in the time available. Gnns and ODEs are in the title of the paper but are barely mentioned in the text. \n2. The methodological contribution is limited\n3. The model is trained in a supervised way meaning that it cannot learn new behaviours or extrapolate beyond the training regime. As this was stated as the main limitation of previous works it suggests this isn’t adding anything beyond these?\n4. Results are based on validating relative to simple simulations - and run time is apparently anyway slow, so what is the value of the proposed approach\n\nQUESTIONS:\n1. The main contribution seems to be to use a fully connected network to learn the force terms through a data term that forces the model to match the simulation results. Why not use a Physics informed neural network to embed the physics into the model, and thus hopefully extrapolate beyond the training regime?\n2. Wouldn’t it make more sense to model this as a graph ODE? http://arxiv.org/pdf/1911.07532\n3. It would help future readers if the authors explain in more detail how the whole network is trained - including where the gnn and neural ODE are called (it took me a long time to work this out as they are only briefly mentioned in the text) \n4. This paper seems like it might be relevant and seems to be going beyond what is proposed here through learning models of interactions https://arxiv.org/abs/2303.09906 with PiNNs - can the authors explain the advs/disadvs of their work relative to an approach such as this\n\nLIMITATIONS:\nLimitations are not really discussed beyond runtimes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-13"}