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Yue Yu 0011

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4 papers

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ICML Conference 2024 Conference Paper

Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws

Ning Liu 0019
Yiming Fan
Xianyi Zeng
Milan Klöwer
Lu Zhang
Yue Yu 0011

Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the governing physical laws directly from data. In contrast to other machine learning applications, partial knowledge is often known a priori about the physical system at hand whereby quantities such as mass, energy and momentum are exactly conserved. Currently, NOs have to learn these conservation laws from data and can only approximately satisfy them due to finite training data and random noise. In this work, we introduce conservation law-encoded neural operators (clawNOs), a suite of NOs that endow inference with automatic satisfaction of such conservation laws. ClawNOs are built with a divergence-free prediction of the solution field, with which the continuity equation is automatically guaranteed. As a consequence, clawNOs are compliant with the most fundamental and ubiquitous conservation laws essential for correct physical consistency. As demonstrations, we consider a wide variety of scientific applications ranging from constitutive modeling of material deformation, incompressible fluid dynamics, to atmospheric simulation. ClawNOs significantly outperform the state-of-the-art NOs in learning efficacy, especially in small-data regimes.

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ICML Conference 2022 Conference Paper

IDYNO: Learning Nonparametric DAGs from Interventional Dynamic Data

Tian Gao 0007
Debarun Bhattacharjya
Elliot Nelson
Miao Liu 0001
Yue Yu 0011

Causal discovery in the form of a directed acyclic graph (DAG) for time series data has been widely studied in various domains. The resulting DAG typically represents a dynamic Bayesian network (DBN), capturing both the instantaneous and time-delayed relationships among variables of interest. We propose a new algorithm, IDYNO, to learn the DAG structure from potentially nonlinear times series data by using a continuous optimization framework that includes a recent formulation for continuous acyclicity constraint. The proposed algorithm is designed to handle both observational and interventional time series data. We demonstrate the promising performance of our method on synthetic benchmark datasets against state-of-the-art baselines. In addition, we show that the proposed method can more accurately learn the underlying structure of a sequential decision model, such as a Markov decision process, with a fixed policy in typical continuous control tasks.

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ICML Conference 2021 Conference Paper

DAGs with No Curl: An Efficient DAG Structure Learning Approach

Yue Yu 0011
Tian Gao 0007
Naiyu Yin
Qiang Ji

Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve efficiency, we propose a novel learning framework to model and learn the weighted adjacency matrices in the DAG space directly. Specifically, we first show that the set of weighted adjacency matrices of DAGs are equivalent to the set of weighted gradients of graph potential functions, and one may perform structure learning by searching in this equivalent set of DAGs. To instantiate this idea, we propose a new algorithm, DAG-NoCurl, which solves the optimization problem efficiently with a two-step procedure: $1)$ first we find an initial non-acyclic solution to the optimization problem, and $2)$ then we employ the Hodge decomposition of graphs and learn an acyclic graph by projecting the non-acyclic graph to the gradient of a potential function. Experimental studies on benchmark datasets demonstrate that our method provides comparable accuracy but better efficiency than baseline DAG structure learning methods on both linear and generalized structural equation models, often by more than one order of magnitude.

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ICML Conference 2019 Conference Paper

DAG-GNN: DAG Structure Learning with Graph Neural Networks

Yue Yu 0011
Jie Chen 0007
Tian Gao 0007
Mo Yu

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al. , 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at \url{https: //github. com/fishmoon1234/DAG-GNN}.

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