Network-based physical simulator

On February 2 1 2020, DeepMind Lab of Google Company published a preprinted article "Learning to Simulate Complex Physics with Graph Network" on arxiv. Researchers have proposed a general framework for simulating complex physical processes, including the interaction of fluids, rigid solids and deformable materials. This framework is called Graphical Network Based Simulator (GNS). This framework uses the nodes in the graph to represent the state of the physical system, and calculates the dynamics of the nodes by learning the process of message passing. This model can predict the state of thousands of particles. By inputting different initial conditions, the particle changes in thousands of time steps can be predicted. The main factors that determine the long-term performance of the model are the steps of information transmission and the destruction of training data by artificially adding noise, so as to reduce the accumulation of errors and prevent over-fitting. The author claims that GNS framework is by far the most accurate and universal physical simulator.

? Simulating complex physical processes in the real world is a very important part of many disciplines, such as engineering mechanics and earth science. However, the traditional simulator is very expensive to create and use. Take ECMWF in european centre for medium-range weather forecasts and NOAA in the United States for example, they must calculate the global high-resolution meteorological and ocean conditions before the forecast period, otherwise the forecast will lose its significance. Therefore, many supercomputers and supporting power facilities have been running. Among them, the theoretical operation speed of P-class "supercomputer" exceeds 2000 trillion times per second. It is conceivable that its forecast products are expensive. Therefore, China Meteorological Bureau spends hundreds of millions of yuan on ECMWF weather forecast products every year (the difference method used in ECMWF forecast is advanced). Because the ocean and atmosphere are both viscous fluids, high-quality hydrodynamic simulation needs a lot of computing resources, which makes it very difficult to expand its application scope.

? It may take many years to build a simulator, and usually its application process must be set in a narrow range, that is, to exchange universality for accuracy. For example, the mesoscale meteorological model WRF was developed by scientific research institutions such as NCEP and NCAR in 2000. Over the past 20 years, it has been constantly updated, fixed and optimized. Running debug in WRF mode is a nightmare for many people. When running a meteorological model, every researcher should adjust the model parameters according to his own research fields and problems, so as to get accurate results at the expense of universality.

? Even the best simulator is often inaccurate because of its poor understanding of the underlying physical process and chaotic parameter setting. For example, although the traditional numerical model has always looked down on the blind parameter adjustment of deep learning, the atmospheric numerical model obtains the best results by constantly adjusting parameters when choosing cloud theory and boundary layer scheme. The difference is that deep learning is post-tuning, and the numerical model is first tuning.

? An attractive way to replace the traditional simulator is to use machine learning to train the simulator directly from the observed data. However, the huge time, space dimension and complex dynamic process have always been difficult for standard end-to-end learning methods to overcome. Space-time dimension is a prominent feature of earth science, and complex dynamic process is the capital and pillar of traditional numerical model.

? In this paper, the author proposes a general framework for learning and simulating from spatiotemporal four-dimensional data, which is called Graphical Network Simulator (GNS). This framework imposes a strong inductive bias, in which the rich physical states are approximated by the graph structure of the interaction between particles, that is, the information transmission between nodes.

? The simulation process of GNS is a trinity model of coding-processing-decoding, end-to-end and messaging network. GNS uses its learned dynamic model dθ and fixed update encoder to predict the future state of particles. Dθ uses the scheme of "encoding-processing-decoding" to calculate the dynamic information y from the input state X. First, an encoder constructs a potential graph structure G0 from the input state X, and then a processor learns the GM on G0, G 1 ..., G0 in m rounds. Finally, the decoder extracts dynamic information y from the final graphic structure GM.

? The simulator used in this paper is based on particle simulation and is widely used in computational fluid dynamics and computer graphics. The dynamic process is calculated according to the interaction of particles in their local neighborhood. The common particle-based fluid simulation method is "smoothed particle hydrodynamics" (SPH), which evaluates the pressure and viscosity around each particle and updates the velocity and position of the particle accordingly. Other technologies, such as position-based dynamics (PBD) and point of matter method (MPM), are more suitable for interacting deformable materials. In PBD, incompressibility and collision dynamics involve solving the double distance constraint between particles and directly predicting their position changes. Recently, some more convenient particle-based differentiable simulation engines have appeared, such as DiffTaichi.

? Graphical network (GN) is a kind of graphical neural network, which has recently been proved to be very effective in learning the interaction between many entities. GN Mapping the input graph to the output graph with the same structure but different node, edge and graph-level attributes can train and learn the form of message passing, so that information can spread between nodes through edges. GN can simulate rigid body, mass spring and robot control system. If the machine wants to achieve the same wisdom as human beings, then the knowledge stored in the machine should not be linear and regular data, such as matrix or vector, but should be stored in the form of graphic structure like the knowledge in the human brain. The brain can simulate all kinds of complex movements, relying on neural networks rather than complex mechanical formulas.

? The author uses the particle-based method to express the dynamic process through the interaction of energy and momentum between particles. However, in practical application scenarios, the physical process is often very complicated. For example, the upper atmosphere is chaotic and nonlinear, while the atmosphere in the boundary layer involves friction. For such a complex system as the atmosphere, long-term step-by-step simulation will lead to error accumulation, that is, computational noise will be introduced. Generally speaking, after more than 300 time steps, the calculation error will lead to the failure of convergence of mathematical and physical equations. Therefore, it is impossible to simply use the calculation result of the previous step as input to predict the state at the next moment. Random walk noise can be introduced to reduce the calculation error.