24 research outputs found
Crystal Structure Search with Random Relaxations Using Graph Networks
Materials design enables technologies critical to humanity, including
combating climate change with solar cells and batteries. Many properties of a
material are determined by its atomic crystal structure. However, prediction of
the atomic crystal structure for a given material's chemical formula is a
long-standing grand challenge that remains a barrier in materials design. We
investigate a data-driven approach to accelerating ab initio random structure
search (AIRSS), a state-of-the-art method for crystal structure search. We
build a novel dataset of random structure relaxations of Li-Si battery anode
materials using high-throughput density functional theory calculations. We
train graph neural networks to simulate relaxations of random structures. Our
model is able to find an experimentally verified structure of Li15Si4 it was
not trained on, and has potential for orders of magnitude speedup over AIRSS
when searching large unit cells and searching over multiple chemical
stoichiometries. Surprisingly, we find that data augmentation of adding
Gaussian noise improves both the accuracy and out of domain generalization of
our models.Comment: Removed citations from the abstract, paper content is unchange
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural networks (GNNs) have gained popularity in this area since graphs offer a natural way of modeling particle interactions and provide a clear way of discretizing the continuum models. However, the graphs constructed for approximating such tasks usually ignore long-range interactions due to unfavorable scaling of the computational complexity with respect to the number of nodes. The errors due to these approximations scale with the discretization of the system, thereby not allowing for generalization under mesh-refinement. Inspired by the classical multipole methods, we purpose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Our multi-level formulation is equivalent to recursively adding inducing points to the kernel matrix, unifying GNNs with multi-resolution matrix factorization of the kernel. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time
Efficient Generation of Multimodal Fluid Simulation Data
Applying the representational power of machine learning to the prediction of
complex fluid dynamics has been a relevant subject of study for years. However,
the amount of available fluid simulation data does not match the notoriously
high requirements of machine learning methods. Researchers have typically
addressed this issue by generating their own datasets, preventing a consistent
evaluation of their proposed approaches. Our work introduces a generation
procedure for synthetic multi-modal fluid simulations datasets. By leveraging a
GPU implementation, our procedure is also efficient enough that no data needs
to be exchanged between users, except for configuration files required to
reproduce the dataset. Furthermore, our procedure allows multiple modalities
(generating both geometry and photorealistic renderings) and is general enough
for it to be applied to various tasks in data-driven fluid simulation. We then
employ our framework to generate a set of thoughtfully designed benchmark
datasets, which attempt to span specific fluid simulation scenarios in a
meaningful way. The properties of our contributions are demonstrated by
evaluating recently published algorithms for the neural fluid simulation and
fluid inverse rendering tasks using our benchmark datasets. Our contribution
aims to fulfill the community's need for standardized benchmarks, fostering
research that is more reproducible and robust than previous endeavors.Comment: 10 pages, 7 figure
Causal Discovery in Physical Systems from Videos
Causal discovery is at the core of human cognition. It enables us to reason about the environment and make counterfactual predictions about unseen scenarios that can vastly differ from our previous experiences. We consider the task of causal discovery from videos in an end-to-end fashion without supervision on the ground-truth graph structure. In particular, our goal is to discover the structural dependencies among environmental and object variables: inferring the type and strength of interactions that have a causal effect on the behavior of the dynamical system. Our model consists of (a) a perception module that extracts a semantically meaningful and temporally consistent keypoint representation from images, (b) an inference module for determining the graph distribution induced by the detected keypoints, and (c) a dynamics module that can predict the future by conditioning on the inferred graph. We assume access to different configurations and environmental conditions, i.e., data from unknown interventions on the underlying system; thus, we can hope to discover the correct underlying causal graph without explicit interventions. We evaluate our method in a planar multi-body interaction environment and scenarios involving fabrics of different shapes like shirts and pants. Experiments demonstrate that our model can correctly identify the interactions from a short sequence of images and make long-term future predictions. The causal structure assumed by the model also allows it to make counterfactual predictions and extrapolate to systems of unseen interaction graphs or graphs of various sizes
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for
simulating physical systems and solving partial differential equations (PDEs)
is formulating physics-based data in the desired structure for neural networks.
Graph neural networks (GNNs) have gained popularity in this area since graphs
offer a natural way of modeling particle interactions and provide a clear way
of discretizing the continuum models. However, the graphs constructed for
approximating such tasks usually ignore long-range interactions due to
unfavorable scaling of the computational complexity with respect to the number
of nodes. The errors due to these approximations scale with the discretization
of the system, thereby not allowing for generalization under mesh-refinement.
Inspired by the classical multipole methods, we propose a novel multi-level
graph neural network framework that captures interaction at all ranges with
only linear complexity. Our multi-level formulation is equivalent to
recursively adding inducing points to the kernel matrix, unifying GNNs with
multi-resolution matrix factorization of the kernel. Experiments confirm our
multi-graph network learns discretization-invariant solution operators to PDEs
and can be evaluated in linear time