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Capitalizing on the remarkable advancements in Large Language Models (LLMs), there is a burgeoning initiative to harness LLMs for instruction following robotic navigation. Such a trend underscores the potential of LLMs to generalize navigational reasoning and diverse language understanding. However, a significant discrepancy in agent performance is observed when integrating LLMs in the Vision-and-Language navigation (VLN) tasks compared to previous downstream specialist models. Furthermore, the inherent capacity of language to interpret and facilitate communication in agent interactions is often underutilized in these integrations. In this work, we strive to bridge the divide between VLN-specialized models and LLM-based navigation paradigms, while maintaining the interpretative prowess of LLMs in generating linguistic navigational reasoning. By aligning visual content in a frozen LLM, we encompass visual observation comprehension for LLMs and exploit a way to incorporate LLMs and navigation policy networks for effective action predictions and navigational reasoning. We demonstrate the data efficiency of the proposed methods and eliminate the gap between LM-based agents and state-of-the-art VLN specialists., Comment: Accepted to ECCV 2024

Vision-and-Language Navigation (VLN) has gained increasing attention over recent years and many approaches have emerged to advance their development. The remarkable achievements of foundation models have shaped the challenges and proposed methods for VLN research. In this survey, we provide a top-down review that adopts a principled framework for embodied planning and reasoning, and emphasizes the current methods and future opportunities leveraging foundation models to address VLN challenges. We hope our in-depth discussions could provide valuable resources and insights: on one hand, to milestone the progress and explore opportunities and potential roles for foundation models in this field, and on the other, to organize different challenges and solutions in VLN to foundation model researchers., Comment: Authors contributed equally to this work, and supervisors contributed equal advising to this work

Machine Learning Force Fields (MLFFs) are of great importance for chemistry, physics, materials science, and many other related fields. The Clebsch-Gordan Transform (CG transform) effectively encodes many-body interactions and is thus an important building block for many models of MLFFs. However, the permutation-equivariance requirement of MLFFs limits the design space of CG transform, that is, intensive CG transform has to be conducted for each neighboring edge and the operations should be performed in the same manner for all edges. This constraint results in reduced expressiveness of the model while simultaneously increasing computational demands. To overcome this challenge, we first implement the CG transform layer on the permutation-invariant abstract edges generated from real edge information. We show that this approach allows complete freedom in the design of the layer without compromising the crucial symmetry. Developing on this free design space, we further propose group CG transform with sparse path, abstract edges shuffling, and attention enhancer to form a powerful and efficient CG transform layer. Our method, known as FreeCG, achieves state-of-the-art (SOTA) results in force prediction for MD17, rMD17, MD22, and is well extended to property prediction in QM9 datasets with several improvements greater than 15% and the maximum beyond 20%. The extensive real-world applications showcase high practicality. FreeCG introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric neural network designs. To demonstrate this, the recent SOTA, QuinNet, is also enhanced under our paradigm. Code will be publicly available., Comment: 25 pages, 8 tables, 11 figures

In this study, we introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model, which incorporates Deep Equilibrium Models (DEQs) for predicting Density Functional Theory (DFT) Hamiltonians. The DEQH model inherently captures the self-consistency nature of Hamiltonian, a critical aspect often overlooked by traditional machine learning approaches for Hamiltonian prediction. By employing DEQ within our model architecture, we circumvent the need for DFT calculations during the training phase to introduce the Hamiltonian's self-consistency, thus addressing computational bottlenecks associated with large or complex systems. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians. When benchmarked on the MD17 and QH9 datasets, DEQHNet, an instantiation of the DEQH framework, has demonstrated a significant improvement in prediction accuracy. Beyond a predictor, the DEQH model is a Hamiltonian solver, in the sense that it uses the fixed-point solving capability of the deep equilibrium model to iteratively solve for the Hamiltonian. Ablation studies of DEQHNet further elucidate the network's effectiveness, offering insights into the potential of DEQ-integrated networks for Hamiltonian learning. We open source our implementation at https://github.com/Zun-Wang/DEQHNet.

In this paper, we develop SE3Set, an SE(3) equivariant hypergraph neural network architecture tailored for advanced molecular representation learning. Hypergraphs are not merely an extension of traditional graphs; they are pivotal for modeling high-order relationships, a capability that conventional equivariant graph-based methods lack due to their inherent limitations in representing intricate many-body interactions. To achieve this, we first construct hypergraphs via proposing a new fragmentation method that considers both chemical and three-dimensional spatial information of molecular system. We then design SE3Set, which incorporates equivariance into the hypergragh neural network. This ensures that the learned molecular representations are invariant to spatial transformations, thereby providing robustness essential for accurate prediction of molecular properties. SE3Set has shown performance on par with state-of-the-art (SOTA) models for small molecule datasets like QM9 and MD17. It excels on the MD22 dataset, achieving a notable improvement of approximately 20% in accuracy across all molecules, which highlights the prevalence of complex many-body interactions in larger molecules. This exceptional performance of SE3Set across diverse molecular structures underscores its transformative potential in computational chemistry, offering a route to more accurate and physically nuanced modeling.

We introduce InternVideo2, a new family of video foundation models (ViFM) that achieve the state-of-the-art results in video recognition, video-text tasks, and video-centric dialogue. Our core design is a progressive training approach that unifies the masked video modeling, crossmodal contrastive learning, and next token prediction, scaling up the video encoder size to 6B parameters. At the data level, we prioritize spatiotemporal consistency by semantically segmenting videos and generating video-audio-speech captions. This improves the alignment between video and text. Through extensive experiments, we validate our designs and demonstrate superior performance on over 60 video and audio tasks. Notably, our model outperforms others on various video-related dialogue and long video understanding benchmarks, highlighting its ability to reason and comprehend longer contexts. Code and models are available at https://github.com/OpenGVLab/InternVideo/tree/main/InternVideo2/., Comment: a technical report about video understanding (accepted to ECCV2024)

Predicting the mean-field Hamiltonian matrix in density functional theory is a fundamental formulation to leverage machine learning for solving molecular science problems. Yet, its applicability is limited by insufficient labeled data for training. In this work, we highlight that Hamiltonian prediction possesses a self-consistency principle, based on which we propose self-consistency training, an exact training method that does not require labeled data. It distinguishes the task from predicting other molecular properties by the following benefits: (1) it enables the model to be trained on a large amount of unlabeled data, hence addresses the data scarcity challenge and enhances generalization; (2) it is more efficient than running DFT to generate labels for supervised training, since it amortizes DFT calculation over a set of queries. We empirically demonstrate the better generalization in data-scarce and out-of-distribution scenarios, and the better efficiency over DFT labeling. These benefits push forward the applicability of Hamiltonian prediction to an ever-larger scale., Comment: Accepted by ICML 2024

The integration of biomolecular modeling with natural language (BL) has emerged as a promising interdisciplinary area at the intersection of artificial intelligence, chemistry and biology. This approach leverages the rich, multifaceted descriptions of biomolecules contained within textual data sources to enhance our fundamental understanding and enable downstream computational tasks such as biomolecule property prediction. The fusion of the nuanced narratives expressed through natural language with the structural and functional specifics of biomolecules described via various molecular modeling techniques opens new avenues for comprehensively representing and analyzing biomolecules. By incorporating the contextual language data that surrounds biomolecules into their modeling, BL aims to capture a holistic view encompassing both the symbolic qualities conveyed through language as well as quantitative structural characteristics. In this review, we provide an extensive analysis of recent advancements achieved through cross modeling of biomolecules and natural language. (1) We begin by outlining the technical representations of biomolecules employed, including sequences, 2D graphs, and 3D structures. (2) We then examine in depth the rationale and key objectives underlying effective multi-modal integration of language and molecular data sources. (3) We subsequently survey the practical applications enabled to date in this developing research area. (4) We also compile and summarize the available resources and datasets to facilitate future work. (5) Looking ahead, we identify several promising research directions worthy of further exploration and investment to continue advancing the field. The related resources and contents are updating in \url{https://github.com/QizhiPei/Awesome-Biomolecule-Language-Cross-Modeling}., Comment: Survey Paper. 25 pages, 9 figures, and 3 tables

As with the laser interferometer gravitational-wave observatory (LIGO), the matched filtering technique will be critical to the data analysis of gravitational wave detection by space-based detectors, including LISA, Taiji and Tianqin. Waveform templates are the basis for such matched filtering techniques. To construct ready-to-use waveform templates, numerical relativity waveforms are a starting point. Therefore, the accuracy issue of numerical relativity waveforms is critically important. There are many investigations regarding this issue with respect to LIGO. But unfortunately there are few results on this issue with respect to space-based detectors. The current paper investigates this problem. Our results indicate that the existing numerical relativity waveforms are as accurate as 99% with respect to space-based detectors, including LISA, Taiji and Tianqin. Such an accuracy level is comparable to that with respect to LIGO.

With the rapid development of Multi-modal Large Language Models (MLLMs), a number of diagnostic benchmarks have recently emerged to evaluate the comprehension capabilities of these models. However, most benchmarks predominantly assess spatial understanding in the static image tasks, while overlooking temporal understanding in the dynamic video tasks. To alleviate this issue, we introduce a comprehensive Multi-modal Video understanding Benchmark, namely MVBench, which covers 20 challenging video tasks that cannot be effectively solved with a single frame. Specifically, we first introduce a novel static-to-dynamic method to define these temporal-related tasks. By transforming various static tasks into dynamic ones, we enable the systematic generation of video tasks that require a broad spectrum of temporal skills, ranging from perception to cognition. Then, guided by the task definition, we automatically convert public video annotations into multiple-choice QA to evaluate each task. On one hand, such a distinct paradigm allows us to build MVBench efficiently, without much manual intervention. On the other hand, it guarantees evaluation fairness with ground-truth video annotations, avoiding the biased scoring of LLMs. Moreover, we further develop a robust video MLLM baseline, i.e., VideoChat2, by progressive multi-modal training with diverse instruction-tuning data. The extensive results on our MVBench reveal that, the existing MLLMs are far from satisfactory in temporal understanding, while our VideoChat2 largely surpasses these leading models by over 15% on MVBench. All models and data are available at https://github.com/OpenGVLab/Ask-Anything., Comment: CVPR 2024 highlight: updated version with Mistral and better performances for MVBench/NExT-QA/STAR/TVQA/EgoSchema/IntentQA

AI for science (AI4S) is an emerging research field that aims to enhance the accuracy and speed of scientific computing tasks using machine learning methods. Traditional AI benchmarking methods struggle to adapt to the unique challenges posed by AI4S because they assume data in training, testing, and future real-world queries are independent and identically distributed, while AI4S workloads anticipate out-of-distribution problem instances. This paper investigates the need for a novel approach to effectively benchmark AI for science, using the machine learning force field (MLFF) as a case study. MLFF is a method to accelerate molecular dynamics (MD) simulation with low computational cost and high accuracy. We identify various missed opportunities in scientifically meaningful benchmarking and propose solutions to evaluate MLFF models, specifically in the aspects of sample efficiency, time domain sensitivity, and cross-dataset generalization capabilities. By setting up the problem instantiation similar to the actual scientific applications, more meaningful performance metrics from the benchmark can be achieved. This suite of metrics has demonstrated a better ability to assess a model's performance in real-world scientific applications, in contrast to traditional AI benchmarking methodologies. This work is a component of the SAIBench project, an AI4S benchmarking suite. The project homepage is https://www.computercouncil.org/SAIBench.

Recent research in language-guided visual navigation has demonstrated a significant demand for the diversity of traversable environments and the quantity of supervision for training generalizable agents. To tackle the common data scarcity issue in existing vision-and-language navigation datasets, we propose an effective paradigm for generating large-scale data for learning, which applies 1200+ photo-realistic environments from HM3D and Gibson datasets and synthesizes 4.9 million instruction trajectory pairs using fully-accessible resources on the web. Importantly, we investigate the influence of each component in this paradigm on the agent's performance and study how to adequately apply the augmented data to pre-train and fine-tune an agent. Thanks to our large-scale dataset, the performance of an existing agent can be pushed up (+11% absolute with regard to previous SoTA) to a significantly new best of 80% single-run success rate on the R2R test split by simple imitation learning. The long-lasting generalization gap between navigating in seen and unseen environments is also reduced to less than 1% (versus 8% in the previous best method). Moreover, our paradigm also facilitates different models to achieve new state-of-the-art navigation results on CVDN, REVERIE, and R2R in continuous environments., Comment: ICCV 2023

Computational simulation of chemical and biological systems using ab initio molecular dynamics has been a challenge over decades. Researchers have attempted to address the problem with machine learning and fragmentation-based methods. However, the two approaches fail to give a satisfactory description of long-range and many-body interactions, respectively. Inspired by fragmentation-based methods, we propose the Long-Short-Range Message-Passing (LSR-MP) framework as a generalization of the existing equivariant graph neural networks (EGNNs) with the intent to incorporate long-range interactions efficiently and effectively. We apply the LSR-MP framework to the recently proposed ViSNet and demonstrate the state-of-the-art results with up to 40% MAE reduction for molecules in MD22 and Chignolin datasets. Consistent improvements to various EGNNs will also be discussed to illustrate the general applicability and robustness of our LSR-MP framework. The code for our experiments and trained model weights could be found at https://github.com/liyy2/LSR-MP.

Vision-language navigation is a task that requires an agent to follow instructions to navigate in environments. It becomes increasingly crucial in the field of embodied AI, with potential applications in autonomous navigation, search and rescue, and human-robot interaction. In this paper, we propose to address a more practical yet challenging counterpart setting - vision-language navigation in continuous environments (VLN-CE). To develop a robust VLN-CE agent, we propose a new navigation framework, ETPNav, which focuses on two critical skills: 1) the capability to abstract environments and generate long-range navigation plans, and 2) the ability of obstacle-avoiding control in continuous environments. ETPNav performs online topological mapping of environments by self-organizing predicted waypoints along a traversed path, without prior environmental experience. It privileges the agent to break down the navigation procedure into high-level planning and low-level control. Concurrently, ETPNav utilizes a transformer-based cross-modal planner to generate navigation plans based on topological maps and instructions. The plan is then performed through an obstacle-avoiding controller that leverages a trial-and-error heuristic to prevent navigation from getting stuck in obstacles. Experimental results demonstrate the effectiveness of the proposed method. ETPNav yields more than 10% and 20% improvements over prior state-of-the-art on R2R-CE and RxR-CE datasets, respectively. Our code is available at https://github.com/MarSaKi/ETPNav., Comment: Project page: https://github.com/MarSaKi/ETPNav

Recently, it was hypothesized that some supermassive black holes (SMBHs) may couple to the cosmic expansion. The mass of these SMBHs increase as the cubic power of the cosmic scale factor, leaving the energy density of the SMBHs unchanged when the universe expands. However, following general principles of general relativity, namely, locality or junction conditions, we show that the inner part of a gravitationally bounded system is unaware of the cosmic expansion, since the outer solution can be smoothly replaced by an asymptotically flat background. For the same reason, the direct reason that we do not expand with the expansion of the universe is not that we are bound states, but rather we are positioned in a greater gravitationally bounded system, namely the local group., Comment: 14 pages, 2 figures

The gravitational lensing effect at higher order under weak-field approximation is believed to be important to distinguish black holes and other compact objects such as wormholes. The deflection angle of a generic wormhole is difficult to solve analytically; thus approximation methods are implemented. In this paper, we investigate the weak-field deflection angle of a specific wormhole, the Ellis-Bronnikov wormhole, up to the 1/b^4 order. We use different approximation formalisms, study their precision at 1/b^4 order by a comparison to a purely numerical result, and finally rank these formalisms by their accuracy. Moreover, we find that certain formalisms are sensitive to the choice of coordinate system; thus it is important to choose the coordinate system appropriately for the evaluating of lensing physics., Comment: PRD published version

The foundation models have recently shown excellent performance on a variety of downstream tasks in computer vision. However, most existing vision foundation models simply focus on image-level pretraining and adpation, which are limited for dynamic and complex video-level understanding tasks. To fill the gap, we present general video foundation models, InternVideo, by taking advantage of both generative and discriminative self-supervised video learning. Specifically, InternVideo efficiently explores masked video modeling and video-language contrastive learning as the pretraining objectives, and selectively coordinates video representations of these two complementary frameworks in a learnable manner to boost various video applications. Without bells and whistles, InternVideo achieves state-of-the-art performance on 39 video datasets from extensive tasks including video action recognition/detection, video-language alignment, and open-world video applications. Especially, our methods can obtain 91.1% and 77.2% top-1 accuracy on the challenging Kinetics-400 and Something-Something V2 benchmarks, respectively. All of these results effectively show the generality of our InternVideo for video understanding. The code will be released at https://github.com/OpenGVLab/InternVideo ., Comment: technical report

In the technical report, we provide our solution for OGB-LSC 2022 Graph Regression Task. The target of this task is to predict the quantum chemical property, HOMO-LUMO gap for a given molecule on PCQM4Mv2 dataset. In the competition, we designed two kinds of models: Transformer-M-ViSNet which is an geometry-enhanced graph neural network for fully connected molecular graphs and Pretrained-3D-ViSNet which is a pretrained ViSNet by distilling geomeotric information from optimized structures. With an ensemble of 22 models, ViSNet Team achieved the MAE of 0.0723 eV on the test-challenge set, dramatically reducing the error by 39.75% compared with the best method in the last year competition.

In this report, we present our champion solutions to five tracks at Ego4D challenge. We leverage our developed InternVideo, a video foundation model, for five Ego4D tasks, including Moment Queries, Natural Language Queries, Future Hand Prediction, State Change Object Detection, and Short-term Object Interaction Anticipation. InternVideo-Ego4D is an effective paradigm to adapt the strong foundation model to the downstream ego-centric video understanding tasks with simple head designs. In these five tasks, the performance of InternVideo-Ego4D comprehensively surpasses the baseline methods and the champions of CVPR2022, demonstrating the powerful representation ability of InternVideo as a video foundation model. Our code will be released at https://github.com/OpenGVLab/ego4d-eccv2022-solutions, Comment: Technical report in 2nd International Ego4D Workshop@ECCV 2022. Code will be released at https://github.com/OpenGVLab/ego4d-eccv2022-solutions

Geometric deep learning has been revolutionizing the molecular modeling field. Despite the state-of-the-art neural network models are approaching ab initio accuracy for molecular property prediction, their applications, such as drug discovery and molecular dynamics (MD) simulation, have been hindered by insufficient utilization of geometric information and high computational costs. Here we propose an equivariant geometry-enhanced graph neural network called ViSNet, which elegantly extracts geometric features and efficiently models molecular structures with low computational costs. Our proposed ViSNet outperforms state-of-the-art approaches on multiple MD benchmarks, including MD17, revised MD17 and MD22, and achieves excellent chemical property prediction on QM9 and Molecule3D datasets. Additionally, ViSNet achieved the top winners of PCQM4Mv2 track in the OGB-LCS@NeurIPS2022 competition. Furthermore, through a series of simulations and case studies, ViSNet can efficiently explore the conformational space and provide reasonable interpretability to map geometric representations to molecular structures.

This report presents the methods of the winning entry of the RxR-Habitat Competition in CVPR 2022. The competition addresses the problem of Vision-and-Language Navigation in Continuous Environments (VLN-CE), which requires an agent to follow step-by-step natural language instructions to reach a target. We present a modular plan-and-control approach for the task. Our model consists of three modules: the candidate waypoints predictor (CWP), the history enhanced planner and the tryout controller. In each decision loop, CWP first predicts a set of candidate waypoints based on depth observations from multiple views. It can reduce the complexity of the action space and facilitate planning. Then, a history-enhanced planner is adopted to select one of the candidate waypoints as the subgoal. The planner additionally encodes historical memory to track the navigation progress, which is especially effective for long-horizon navigation. Finally, we propose a non-parametric heuristic controller named tryout to execute low-level actions to reach the planned subgoal. It is based on the trial-and-error mechanism which can help the agent to avoid obstacles and escape from getting stuck. All three modules work hierarchically until the agent stops. We further take several recent advances of Vision-and-Language Navigation (VLN) to improve the performance such as pretraining based on large-scale synthetic in-domain dataset, environment-level data augmentation and snapshot model ensemble. Our model won the RxR-Habitat Competition 2022, with 48% and 90% relative improvements over existing methods on NDTW and SR metrics respectively., Comment: Winner of the 2nd RxR-Habitat Competition @ CVPR2022

Most existing works in vision-and-language navigation (VLN) focus on either discrete or continuous environments, training agents that cannot generalize across the two. The fundamental difference between the two setups is that discrete navigation assumes prior knowledge of the connectivity graph of the environment, so that the agent can effectively transfer the problem of navigation with low-level controls to jumping from node to node with high-level actions by grounding to an image of a navigable direction. To bridge the discrete-to-continuous gap, we propose a predictor to generate a set of candidate waypoints during navigation, so that agents designed with high-level actions can be transferred to and trained in continuous environments. We refine the connectivity graph of Matterport3D to fit the continuous Habitat-Matterport3D, and train the waypoints predictor with the refined graphs to produce accessible waypoints at each time step. Moreover, we demonstrate that the predicted waypoints can be augmented during training to diversify the views and paths, and therefore enhance agent's generalization ability. Through extensive experiments we show that agents navigating in continuous environments with predicted waypoints perform significantly better than agents using low-level actions, which reduces the absolute discrete-to-continuous gap by 11.76% Success Weighted by Path Length (SPL) for the Cross-Modal Matching Agent and 18.24% SPL for the Recurrent VLN-BERT. Our agents, trained with a simple imitation learning objective, outperform previous methods by a large margin, achieving new state-of-the-art results on the testing environments of the R2R-CE and the RxR-CE datasets.

We investigate obstacles of superluminal "warp drive" travels from interactions with interstellar matter and from curvature effects. The effect of collision of interstellar dust particles and photons with the spacecraft will all lead to a pressure proportional to the apparent velocity of the spaceship $v_s$. The force exerted on the spacecraft from the curvature effect has two non-trivial components. The radial and longitudinal components scales as $v_s^2$ and $v_s^4$ respectively. The above obstacles become increasingly important when the spaceship travels at high superluminal speeds.

With many frameworks based on message passing neural networks proposed to predict molecular and bulk properties, machine learning methods have tremendously shifted the paradigms of computational sciences underpinning physics, material science, chemistry, and biology. While existing machine learning models have yielded superior performances in many occasions, most of them model and process molecular systems in terms of homogeneous graph, which severely limits the expressive power for representing diverse interactions. In practice, graph data with multiple node and edge types is ubiquitous and more appropriate for molecular systems. Thus, we propose the heterogeneous relational message passing network (HermNet), an end-to-end heterogeneous graph neural networks, to efficiently express multiple interactions in a single model with {\it ab initio} accuracy. HermNet performs impressively against many top-performing models on both molecular and extended systems. Specifically, HermNet outperforms other tested models in nearly 75\%, 83\% and 94\% of tasks on MD17, QM9 and extended systems datasets, respectively. Finally, we elucidate how the design of HermNet is compatible with quantum mechanics from the perspective of the density functional theory. Besides, HermNet is a universal framework, whose sub-networks could be replaced by other advanced models.

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of crystalline materials, aiming to bypass the computationally demanding self-consistent field iterations of DFT and substantially improve the efficiency of ab initio electronic-structure calculations. A general framework is proposed to deal with the large dimensionality and gauge (or rotation) covariance of DFT Hamiltonian matrix by virtue of locality and is realized by the message passing neural network for deep learning. High accuracy, high efficiency and good transferability of the DeepH method are generally demonstrated for various kinds of material systems and physical properties. The method provides a solution to the accuracy-efficiency dilemma of DFT and opens opportunities to explore large-scale material systems, as evidenced by a promising application to study twisted van der Waals materials.

Molecular dynamics is a powerful simulation tool to explore material properties. Most of the realistic material systems are too large to be simulated with first-principles molecular dynamics. Classical molecular dynamics has lower computational cost but requires accurate force fields to achieve chemical accuracy. In this work, we develop a symmetry-adapted graph neural networks framework, named molecular dynamics graph neural networks (MDGNN), to construct force fields automatically for molecular dynamics simulations for both molecules and crystals. This architecture consistently preserves the translation, rotation and permutation invariance in the simulations. We propose a new feature engineering method including higher order contributions and show that MDGNN accurately reproduces the results of both classical and first-principles molecular dynamics. We also demonstrate that force fields constructed by the model has good transferability. Therefore, MDGNN provides an efficient and promising option for molecular dynamics simulations of large scale systems with high accuracy.