Coherent energy and force uncertainty in deep learning force fields

In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely used modeling approach involves predicting both a mean and variance for each energy value. However, this model is not differentiable under the usual white noise assumption, so energy uncertainty does not naturally translate to force uncertainty. In this work we propose a machine learning potential energy model in which energy and force aleatoric uncertainty are linked through a spatially correlated noise process. We demonstrate our approach on an equivariant messages passing neural network potential trained on energies and forces on two out-of-equilibrium molecular datasets. Furthermore, we also show how to obtain epistemic uncertainties in this setting based on a Bayesian interpretation of deep ensemble models.

Multi-view self-supervised learning for multivariate variable-channel time series

Labeling of multivariate biomedical time series data is a laborious and expensive process. Self-supervised contrastive learning alleviates the need for large, labeled datasets through pretraining on unlabeled data. However, for multivariate time series data, the set of input channels often varies between applications, and most existing work does not allow for transfer between datasets with different sets of input channels. We propose learning one encoder to operate on all input channels individually. We then use a message passing neural network to extract a single representation across channels. We demonstrate the potential of this method by pretraining our model on a dataset with six EEG channels and then fine-tuning it on a dataset with two different EEG channels. We compare models with and without the message passing neural network across different contrastive loss functions. We show that our method, combined with the TS2Vec loss, outperforms all other methods in most settings.

Synthetic data shuffling accelerates the convergence of federated learning under data heterogeneity

In federated learning, data heterogeneity is a critical challenge. A straightforward solution is to shuffle the clients' data to homogenize the distribution. However, this may violate data access rights, and how and when shuffling can accelerate the convergence of a federated optimization algorithm is not theoretically well understood. In this paper, we establish a precise and quantifiable correspondence between data heterogeneity and parameters in the convergence rate when a fraction of data is shuffled across clients. We prove that shuffling can quadratically reduce the gradient dissimilarity with respect to the shuffling percentage, accelerating convergence. Inspired by the theory, we propose a practical approach that addresses the data access rights issue by shuffling locally generated synthetic data. The experimental results show that shuffling synthetic data improves the performance of multiple existing federated learning algorithms by a large margin.

Graph Neural Network Interatomic Potential Ensembles with Calibrated Aleatoric and Epistemic Uncertainty on Energy and Forces

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

Partial Variance Reduction improves Non-Convex Federated learning on heterogeneous data

Data heterogeneity across clients is a key challenge in federated learning. Prior works address this by either aligning client and server models or using control variates to correct client model drift. Although these methods achieve fast convergence in convex or simple non-convex problems, the performance in over-parameterized models such as deep neural networks is lacking. In this paper, we first revisit the widely used FedAvg algorithm in a deep neural network to understand how data heterogeneity influences the gradient updates across the neural network layers. We observe that while the feature extraction layers are learned efficiently by FedAvg, the substantial diversity of the final classification layers across clients impedes the performance. Motivated by this, we propose to correct model drift by variance reduction only on the final layers. We demonstrate that this significantly outperforms existing benchmarks at a similar or lower communication cost. We furthermore provide proof for the convergence rate of our algorithm.

Raman Spectrum Matching with Contrastive Representation Learning

Raman spectroscopy is an effective, low-cost, non-intrusive technique often used for chemical identification. Typical approaches are based on matching observations to a reference database, which requires careful preprocessing, or supervised machine learning, which requires a fairly large number of training observations from each class. We propose a new machine learning technique for Raman spectrum matching, based on contrastive representation learning, that requires no preprocessing and works with as little as a single reference spectrum from each class. On three datasets we demonstrate that our approach significantly improves or is on par with the state of the art in prediction accuracy, and we show how to compute conformal prediction sets with specified frequentist coverage. Based on our findings, we believe contrastive representation learning is a promising alternative to existing methods for Raman spectrum matching.

Calibrated Uncertainty for Molecular Property Prediction using Ensembles of Message Passing Neural Networks

Data-driven methods based on machine learning have the potential to accelerate analysis of atomic structures. However, machine learning models can produce overconfident predictions and it is therefore crucial to detect and handle uncertainty carefully. Here, we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. The method presented in this paper differs from the previous work by considering both aleatoric and epistemic uncertainty in a unified framework, and by re-calibrating the predictive distribution on unseen data. Through computer experiments, we show that our approach results in accurate models for predicting molecular formation energies with calibrated uncertainty in and out of the training data distribution on two public molecular benchmark datasets, QM9 and PC9. The proposed method provides a general framework for training and evaluating neural network ensemble models that are able to produce accurate predictions of properties of molecules with calibrated uncertainty.

Materials property prediction using symmetry-labeled graphs as atomic-position independent descriptors

Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning models for prediction of DFT calculated properties are currently of interest. A particular challenge for \emph{new} materials is that the atomic positions are generally not known. We present a machine learning model for the prediction of DFT-calculated formation energies based on Voronoi quotient graphs and local symmetry classification without the need for detailed information about atomic positions. The model is implemented as a message passing neural network and tested on the Open Quantum Materials Database (OQMD) and the Materials Project database. The test mean absolute error is 20 meV on the OQMD database and 40 meV on Materials Project Database. The possibilities for prediction in a realistic computational screening setting is investigated on a dataset of 5976 ABSe$_3$ selenides with very limited overlap with the OQMD training set. Pretraining on OQMD and subsequent training on 100 selenides result in a mean absolute error below 0.1 eV for the formation energy of the selenides.

Probabilistic PARAFAC2

The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable in order to improve robustness to noise and provide a well founded principle for determining the number of factors, but challenging because the factor loadings are constrained to be orthogonal. We develop two probabilistic formulations of the PARAFAC2 along with variational procedures for inference: In the one approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the other, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulation to the conventional direct fitting algorithm based on maximum likelihood. On simulated data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data, we compare our approach to the conventional PARAFAC2 model estimation and find that the probabilistic formulation is more robust to noise and model order misspecification. The probabilistic PARAFAC2 thus forms a promising framework for modeling multi-way data accounting for uncertainty.