A Neural Network Subgrid Model of the Early Stages of Planet Formation

Planet formation is a multi-scale process in which the coagulation of $\mathrm{\mu m}$-sized dust grains in protoplanetary disks is strongly influenced by the hydrodynamic processes on scales of astronomical units ($\approx 1.5\times 10^8 \,\mathrm{km}$). Studies are therefore dependent on subgrid models to emulate the micro physics of dust coagulation on top of a large scale hydrodynamic simulation. Numerical simulations which include the relevant physical effects are complex and computationally expensive. Here, we present a fast and accurate learned effective model for dust coagulation, trained on data from high resolution numerical coagulation simulations. Our model captures details of the dust coagulation process that were so far not tractable with other dust coagulation prescriptions with similar computational efficiency.Comment: 6 pages, 4 figures, accepted at the Machine Learning and the Physical Sciences workshop, NeurIPS 202

Privacy and Transparency in Graph Machine Learning: A Unified Perspective

Graph Machine Learning (GraphML), whereby classical machine learning is generalized to irregular graph domains, has enjoyed a recent renaissance, leading to a dizzying array of models and their applications in several domains. With its growing applicability to sensitive domains and regulations by government agencies for trustworthy AI systems, researchers have started looking into the issues of transparency and privacy of graph learning. However, these topics have been mainly investigated independently. In this position paper, we provide a unified perspective on the interplay of privacy and transparency in GraphML

Three-dimensional granular flow simulation using graph neural network-based learned simulator

Reliable evaluations of geotechnical hazards like landslides and debris flow require accurate simulation of granular flow dynamics. Traditional numerical methods can simulate the complex behaviors of such flows that involve solid-like to fluid-like transitions, but they are computationally intractable when simulating large-scale systems. Surrogate models based on statistical or machine learning methods are a viable alternative, but they are typically empirical and rely on a confined set of parameters in evaluating associated risks. Due to their permutation-dependent learning, conventional machine learning models require an unreasonably large amount of training data for building generalizable surrogate models. We employ a graph neural network (GNN), a novel deep learning technique, to develop a GNN-based simulator (GNS) for granular flows to address these issues. Graphs represent the state of granular flows and interactions, like the exchange of energy and momentum between grains, and GNN learns the local interaction law. GNS takes the current state of the granular flow and estimates the next state using Euler explicit integration. We train GNS on a limited set of granular flow trajectories and evaluate its performance in a three-dimensional granular column collapse domain. GNS successfully reproduces the overall behaviors of column collapses with various aspect ratios that were not encountered during training. The computation speed of GNS outperforms high-fidelity numerical simulators by 300 times

Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systems

Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce Variational Integrator Graph Networks - a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single and many-body problems studied in recent literature. We empirically show that the improvements arise because high order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the Partitioned Runge-Kutta method.Comment: updated version that includes an extensive ablation across graph,non-graph methods as well as different integrators [under review

Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media

Numerical simulation of multi-phase fluid dynamics in porous media is critical for many subsurface applications. Data-driven surrogate modeling provides computationally inexpensive alternatives to high-fidelity numerical simulators. While the commonly used convolutional neural networks (CNNs) are powerful in approximating partial differential equation solutions, it remains challenging for CNNs to handle irregular and unstructured simulation meshes. However, subsurface simulation models often involve unstructured meshes with complex mesh geometries, which limits the application of CNNs. To address this challenge, here we construct surrogate models based on Graph Convolutional Networks (GCNs) to approximate the spatial-temporal solutions of multi-phase flow and transport processes. We propose a new GCN architecture suited to the hyperbolic character of the coupled PDE system, to better capture the saturation dynamics. Results of 2D heterogeneous test cases show that our surrogates predict the evolutions of the pressure and saturation states with high accuracy, and the predicted rollouts remain stable for multiple timesteps. Moreover, the GCN-based models generalize well to irregular domain geometries and unstructured meshes that are unseen in the training dataset

Integrating Pentatonic Angklung into Physics Experiment to Identify Multiple Representation Skills in Junior High School

Angklung is a traditional musical instrument from West Java that can be used as a learning medium for sound concepts. The study focuses on pentatonic Angklung as a musical instrument commonly used in Ngaseuk ceremonies as rice planting rituals in the Baduy tribe. This study aims to report the integration of pentatonic Angklung into physics experiments and investigate multiple representation skills. Technology-based mobile used as an experimental tool is Phypox. The designed activity aims to identify multiple representation skills using guided-inquiry models in four stages: Open, Explore, Create, and Share. The study participants are 31 8th-grade students at one of the junior high schools in West Java Province, Indonesia. Experiment activities investigate variables that affect the frequency of the pentatonic Angklung. A worksheet guides experiment activities following the syntax of the guided-inquiry model. The study results show that students use different representations at each stage in the worksheet. Students use four representations in this experimental activity: verbal, mathematical, pictorial, and graphical. It can be concluded that integrating pentatonic Angklung into physics experiments can identify students' multiple representation skills in junior high school