TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts.Comment: 20 pages, 8 figures, 5 table

Coarse-Graining Auto-Encoders for Molecular Dynamics

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and spatial scales involved in thermodynamic and kinetic phenomena in materials, atomistic simulations are often computationally unfeasible. Coarse-graining methods allow simulating larger systems, by reducing the dimensionality of the simulation, and propagating longer timesteps, by averaging out fast motions. Coarse-graining involves two coupled learning problems; defining the mapping from an all-atom to a reduced representation, and the parametrization of a Hamiltonian over coarse-grained coordinates. Multiple statistical mechanics approaches have addressed the latter, but the former is generally a hand-tuned process based on chemical intuition. Here we present Autograin, an optimization framework based on auto-encoders to learn both tasks simultaneously. Autograin is trained to learn the optimal mapping between all-atom and reduced representation, using the reconstruction loss to facilitate the learning of coarse-grained variables. In addition, a force-matching method is applied to variationally determine the coarse-grained potential energy function. This procedure is tested on a number of model systems including single-molecule and bulk-phase periodic simulations.Comment: 8 pages, 6 figure

Learning Deep Structured Models

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to combine MRFs with deep learning algorithms to estimate complex representations while taking into account the dependencies between the output random variables. Towards this goal, we propose a training algorithm that is able to learn structured models jointly with deep features that form the MRF potentials. Our approach is efficient as it blends learning and inference and makes use of GPU acceleration. We demonstrate the effectiveness of our algorithm in the tasks of predicting words from noisy images, as well as multi-class classification of Flickr photographs. We show that joint learning of the deep features and the MRF parameters results in significant performance gains.Comment: 11 pages including referenc

Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results

Alchemical and structural distribution based representation for improved QML

We introduce a representation of any atom in any chemical environment for the generation of efficient quantum machine learning (QML) models of common electronic ground-state properties. The representation is based on scaled distribution functions explicitly accounting for elemental and structural degrees of freedom. Resulting QML models afford very favorable learning curves for properties of out-of-sample systems including organic molecules, non-covalently bonded protein side-chains, (H$_2$O)$_{40}$-clusters, as well as diverse crystals. The elemental components help to lower the learning curves, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training, as evinced for single, double, and triple bonds among main-group elements

Alchemical and structural distribution based representation for improved QML

We introduce a representation of any atom in any chemical environment for the generation of efficient quantum machine learning (QML) models of common electronic ground-state properties. The representation is based on scaled distribution functions explicitly accounting for elemental and structural degrees of freedom. Resulting QML models afford very favorable learning curves for properties of out-of-sample systems including organic molecules, non-covalently bonded protein side-chains, (H$_2$O)$_{40}$-clusters, as well as diverse crystals. The elemental components help to lower the learning curves, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training, as evinced for single, double, and triple bonds among main-group elements