Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLearning physical properties of anomalous random walks using graph neural networks
71
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical model or class of models of the underlying random walks. Reliable inference is made difficult by the inherent stochastic nature of single particle motion, by experimental noise, and by the short duration of most experimental trajectories. Model identification is further complicated by the fact that main physical properties of random walk models are only defined asymptotically, and are thus degenerate for short trajectories. Here, we introduce a new, fast approach to inferring random walk properties based on graph neural networks (GNNs). Our approach consists in associating a vector of features with each observed position, and a sparse graph structure with each observed trajectory. By performing simulation-based supervised learning on this construct [1], we show that we can reliably learn models of random walks and their anomalous exponents. The method can naturally be applied to trajectories of any length. We show its efficiency in analysing various anomalous random walks of biological relevance that were proposed in the AnDi challenge [2]. We explore how information is encoded in the GNN, and we show that it learns relevant physical features of the random walks. We furthermore evaluate its ability to generalize to types of trajectories not seen during training, and we show that the GNN retains high accuracy even with few parameters. We finally discuss the possibility to leverage these networks to analyse experimental data.
rate research
Read More
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator -- a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as Generalized Regularized Interaction Screening Estimator (GRISE). But the computational cost of GRISE becomes prohibitive when the energy function of the true graphical model has higher-order terms. We introduce NeurISE, a neural net based algorithm for graphical model learning, to tackle this limitation of GRISE. We use neural nets as function approximators in an Interaction Screening objective function. The optimization of this objective then produces a neural-net representation for the conditionals of the graphical model. NeurISE algorithm is seen to be a better alternative to GRISE when the energy function of the true model has a high order with a high degree of symmetry. In these cases NeurISE is able to find the correct parsimonious representation for the conditionals without being fed any prior information about the true model. NeurISE can also be used to learn the underlying structure of the true model with some simple modifications to its training procedure. In addition, we also show a variant of NeurISE that can be used to learn a neural net representation for the full energy function of the true model.
We apply a temporal edge prediction model for weighted dynamic graphs to predict time-dependent changes in molecular structure. Each molecule is represented as a complete graph in which each atom is a vertex and all vertex pairs are connected by an edge weighted by the Euclidean distance between atom pairs. We ingest a sequence of complete molecular graphs into a dynamic graph neural network (GNN) to predict the graph at the next time step. Our dynamic GNN predicts atom-to-atom distances with a mean absolute error of 0.017 r{A}, which is considered ``chemically accurate for molecular simulations. We also explored the transferability of a trained network to new molecular systems and found that finetuning with less than 10% of the total trajectory provides a mean absolute error of the same order of magnitude as that when training from scratch on the full molecular trajectory.
We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.
Despite tremendous success of deep neural network in machine learning, the underlying reason for its superior learning capability remains unclear. Here, we present a framework based on statistical physics to study dynamics of stochastic gradient descent (SGD) that drives learning in neural networks. By using the minibatch gradient ensemble, we construct order parameters to characterize dynamics of weight updates in SGD. Without mislabeled data, we find that the SGD learning dynamics transitions from a fast learning phase to a slow exploration phase, which is associated with large changes in order parameters that characterize the alignment of SGD gradients and their mean amplitude. In the case with randomly mislabeled samples, SGD learning dynamics falls into four distinct phases. The system first finds solutions for the correctly labeled samples in phase I, it then wanders around these solutions in phase II until it finds a direction to learn the mislabeled samples during phase III, after which it finds solutions that satisfy all training samples during phase IV. Correspondingly, the test error decreases during phase I and remains low during phase II; however, it increases during phase III and reaches a high plateau during phase IV. The transitions between different phases can be understood by changes of order parameters that characterize the alignment of mean gradients for the correctly and incorrectly labeled samples and their (relative) strength during learning. We find that individual sample losses for the two datasets are most separated during phase II, which leads to a cleaning process to eliminate mislabeled samples for improving generalization.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
