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The use of machine learning for material property prediction and discovery has traditionally centered on graph neural networks that incorporate the geometric configuration of all atoms. However, in practice not all this information may be readily available, e.g.~when evaluating the potentially unknown binding of adsorbates to catalyst. In this paper, we investigate whether it is possible to predict a system's relaxed energy in the OC20 dataset while ignoring the relative position of the adsorbate with respect to the electro-catalyst. We consider SchNet, DimeNet++ and FAENet as base architectures and measure the impact of four modifications on model performance: removing edges in the input graph, pooling independent representations, not sharing the backbone weights and using an attention mechanism to propagate non-geometric relative information. We find that while removing binding site information impairs accuracy as expected, modified models are able to predict relaxed energies with remarkably decent MAE. Our work suggests future research directions in accelerated materials discovery where information on reactant configurations can be reduced or altogether omitted.

Introduction: The amount of data generated by original research is growing exponentially. Publicly releasing them is recommended to comply with the Open Science principles. However, data collected from human participants cannot be released as-is without raising privacy concerns. Fully synthetic data represent a promising answer to this challenge. This approach is explored by the French Centre de Recherche en {\'E}pid{\'e}miologie et Sant{\'e} des Populations in the form of a synthetic data generation framework based on Classification and Regression Trees and an original distance-based filtering. The goal of this work was to develop a refined version of this framework and to assess its risk-utility profile with empirical and formal tools, including novel ones developed for the purpose of this evaluation.Materials and Methods: Our synthesis framework consists of four successive steps, each of which is designed to prevent specific risks of disclosure. We assessed its performance by applying two or more of these steps to a rich epidemiological dataset. Privacy and utility metrics were computed for each of the resulting synthetic datasets, which were further assessed using machine learning approaches.Results: Computed metrics showed a satisfactory level of protection against attribute disclosure attacks for each synthetic dataset, especially when the full framework was used. Membership disclosure attacks were formally prevented without significantly altering the data. Machine learning approaches showed a low risk of success for simulated singling out and linkability attacks. Distributional and inferential similarity with the original data were high with all datasets.Discussion: This work showed the technical feasibility of generating publicly releasable synthetic data using a multi-step framework. Formal and empirical tools specifically developed for this demonstration are a valuable contribution to this field. Further research should focus on the extension and validation of these tools, in an effort to specify the intrinsic qualities of alternative data synthesis methods.Conclusion: By successfully assessing the quality of data produced using a novel multi-step synthetic data generation framework, we showed the technical and conceptual soundness of the Open-CESP initiative, which seems ripe for full-scale implementation.

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network parameterizes the solution with time-varying controls to establish a control-to-state regression. Firstly, finite volume scheme is adopted to discretize flow equations and formulate loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states. To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state space equations. We train the network progressively for every timestep, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for subsequent timestep. The proposed model is used to simulate oil-water porous flow scenarios with varying reservoir gridblocks and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The results underscore the potential of PICNN in effectively simulating systems with numerous grid blocks, as computation time does not scale with model dimensionality. We assess the temporal error using 10 different testing controls with variation in magnitude and another 10 with higher alternation frequency with proposed control-to-state architecture. Our observations suggest the need for a more robust and reliable model when dealing with controls that exhibit significant variations in magnitude or frequency.

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of Hamiltonian and Lagrangian of physical systems. While the existing methods parameterize the Lagrangian using neural networks, we propose an alternate framework for learning interpretable Lagrangian descriptions of physical systems from limited data using the sparse Bayesian approach. Unlike existing neural network-based approaches, the proposed approach (a) yields an interpretable description of Lagrangian, (b) exploits Bayesian learning to quantify the epistemic uncertainty due to limited data, (c) automates the distillation of Hamiltonian from the learned Lagrangian using Legendre transformation, and (d) provides ordinary (ODE) and partial differential equation (PDE) based descriptions of the observed systems. Six different examples involving both discrete and continuous system illustrates the efficacy of the proposed approach.

The beneficial role of noise in learning is nowadays a consolidated concept in the field of artificial neural networks, suggesting that even biological systems might take advantage of similar mechanisms to maximize their performance. The training-with-noise algorithm proposed by Gardner and collaborators is an emblematic example of a noise injection procedure in recurrent networks, which are usually employed to model real neural systems. We show how adding structure into noisy training data can substantially improve the algorithm performance, allowing to approach perfect classification and maximal basins of attraction. We also prove that the so-called Hebbian unlearning rule coincides with the training-with-noise algorithm when noise is maximal and data are fixed points of the network dynamics. A sampling scheme for optimal noisy data is eventually proposed and implemented to outperform both the training-with-noise and the Hebbian unlearning procedures.

We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems framed in high-dimensional ambient spaces. We dub the proposed framework GAN-Flow. The proposed method leverages the intrinsic dimension reduction and superior sample generation capabilities of GANs to define a low-dimensional data-driven prior distribution. Once a trained GAN-prior is available, the inverse problem is solved entirely in the latent space of the GAN using variational Bayesian inference with normalizing flow-based variational distribution, which approximates low-dimensional posterior distribution by transforming realizations from the low-dimensional latent prior (Gaussian) to corresponding realizations of a low-dimensional variational posterior distribution. The trained GAN generator then maps realizations from this approximate posterior distribution in the latent space back to the high-dimensional ambient space. We also propose a two-stage training strategy for GAN-Flow wherein we train the two generative models sequentially. Thereafter, GAN-Flow can estimate the statistics of posterior-predictive quantities of interest at virtually no additional computational cost. The synergy between the two types of generative models allows us to overcome many challenges associated with the application of Bayesian inference to large-scale inverse problems, chief among which are describing an informative prior and sampling from the high-dimensional posterior. We demonstrate the efficacy and flexibility of GAN-Flow on various physics-based inverse problems of varying ambient dimensionality and prior knowledge using different types of GANs and normalizing flows.

The High-index saddle dynamics (HiSD) method serves as an efficient tool for computing saddle points and constructing solution landscapes. Nevertheless, the conventional HiSD method often encounters slow convergence rates on ill-conditioned problems. To address this challenge, we propose an accelerated high-index saddle dynamics (A-HiSD) by incorporating the heavy ball method. We prove the linear stability theory of the continuous A-HiSD, and subsequently estimate the local convergence rate for the discrete A-HiSD. Our analysis demonstrates that the A-HiSD method exhibits a faster convergence rate compared to the conventional HiSD method, especially when dealing with ill-conditioned problems. We also perform various numerical experiments including the loss function of neural network to substantiate the effectiveness and acceleration of the A-HiSD method.

We present a machine learning framework capable of consistently inferring mathematical expressions of the hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelasticity model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via PNAM is that (1) it is spanned by a set univariate basis that can be re-parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi-variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning-generated mathematical model also requires fewer arithmetic operations than the deep neural network counterparts during deployment. This latter attribute is crucial for scaling large-scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state-of-the-art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade-off between interpretability, accuracy, and precision of the learned symbolic hyperelasticity models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics-based knowledge.

We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized class of candidate models, the Fisher information of observed sequence probabilities lower-bounds the variance in model estimation from finite data. As sequence-length increases, the minimal variance scales as the square inverse of the length -- with constant coefficient given by the information rate. We discover a simple closed-form expression for this information rate, even in the case of infinite Markov order. We furthermore obtain the exact analytic lower bound on model variance from the observation-induced metadynamic among belief states. We discover ephemeral, exponential, and more general modes of convergence to the asymptotic information rate. Surprisingly, this myopic information rate converges to the asymptotic Fisher information rate with exactly the same relaxation timescales that appear in the myopic entropy rate as it converges to the Shannon entropy rate for the process. We illustrate these results with a sequence of examples that highlight qualitatively distinct features of stochastic processes that shape optimal learning.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.