Topological degree as a discrete diagnostic for disentanglement, with applications to the $Δ$VAE

We investigate the ability of Diffusion Variational Autoencoder ($\Delta$VAE) with unit sphere $\mathcal{S}^2$ as latent space to capture topological and geometrical structure and disentangle latent factors in datasets. For this, we introduce a new diagnostic of disentanglement: namely the topological degree of the encoder, which is a map from the data manifold to the latent space. By using tools from homology theory, we derive and implement an algorithm that computes this degree. We use the algorithm to compute the degree of the encoder of models that result from the training procedure. Our experimental results show that the $\Delta$VAE achieves relatively small LSBD scores, and that regardless of the degree after initialization, the degree of the encoder after training becomes $-1$ or $+1$, which implies that the resulting encoder is at least homotopic to a homeomorphism.

Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates

Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many forward solves, for example in the case of inverse design with many degrees of freedom. In this work, we investigate and extend neural PDE solvers as a tool to aid in scaling simulations for two-phase flow problems, and simulations of oil expulsion from a pore specifically. We extend existing numerical methods for this problem to a more complex setting involving varying geometries of the domain to generate a challenging dataset. Further, we investigate three prominent neural PDE solver methods, namely the UNet, DRN and U-FNO, and extend them for characteristics of the oil-expulsion problem: (1) spatial conditioning on the geometry; (2) periodicity in the boundary; (3) approximate mass conservation. We scale all methods and benchmark their speed-accuracy trade-off, evaluate qualitative properties, and perform an ablation study. We find that the investigated methods can accurately model the droplet dynamics with up to three orders of magnitude speed-up, that our extensions improve performance over the baselines, and that the introduced varying geometries constitute a significantly more challenging setting over the previously considered oil expulsion problem.

Efficient Probabilistic Modeling of Crystallization at Mesoscopic Scale

Crystallization processes at the mesoscopic scale, where faceted, dendritic growth, and multigrain formation can be observed, are of particular interest within materials science and metallurgy. These processes are highly nonlinear, stochastic, and sensitive to small perturbations of system parameters and initial conditions. Methods for the simulation of these processes have been developed using discrete numerical models, but these are computationally expensive. This work aims to scale crystal growth simulation with a machine learning emulator. Specifically, autoregressive latent variable models are well suited for modeling the joint distribution over system parameters and the crystallization trajectories. However, successfully training such models is challenging due to the stochasticity and sensitivity of the system. Existing approaches consequently fail to produce diverse and faithful crystallization trajectories. In this paper, we introduce the Crystal Growth Neural Emulator (CGNE), a probabilistic model for efficient crystal growth emulation at the mesoscopic scale that overcomes these challenges. We validate CGNE results using the morphological properties of the crystals produced by numerical simulation. CGNE delivers a factor of 11 improvement in inference time and performance gains compared with recent state-of-the-art probabilistic models for dynamical systems.

Similarity Equivariant Graph Neural Networks for Homogenization of Metamaterials

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them accurately and quickly, in order to tune their mechanical properties. Since conventional simulations using the finite element method entail a high computational cost, in this article we aim to develop a machine learning-based approach that scales favorably to serve as a surrogate model. To ensure that the model is also able to handle various microstructures, including those not encountered during training, we include the microstructure as part of the network input. Therefore, we introduce a graph neural network that predicts global quantities (energy, stress stiffness) as well as the pattern transformations that occur (the kinematics). To make our model as accurate and data-efficient as possible, various symmetries are incorporated into the model. The starting point is an E(n)-equivariant graph neural network (which respects translation, rotation and reflection) that has periodic boundary conditions (i.e., it is in-/equivariant with respect to the choice of RVE), is scale in-/equivariant, can simulate large deformations, and can predict scalars, vectors as well as second and fourth order tensors (specifically energy, stress and stiffness). The incorporation of scale equivariance makes the model equivariant with respect to the similarities group, of which the Euclidean group E(n) is a subgroup. We show that this network is more accurate and data-efficient than graph neural networks with fewer symmetries. To create an efficient graph representation of the finite element discretization, we use only the internal geometrical hole boundaries from the finite element mesh to achieve a better speed-up and scaling with the mesh size.

VADA: a Data-Driven Simulator for Nanopore Sequencing

Nanopore sequencing offers the ability for real-time analysis of long DNA sequences at a low cost, enabling new applications such as early detection of cancer. Due to the complex nature of nanopore measurements and the high cost of obtaining ground truth datasets, there is a need for nanopore simulators. Existing simulators rely on handcrafted rules and parameters and do not learn an internal representation that would allow for analysing underlying biological factors of interest. Instead, we propose VADA, a purely data-driven method for simulating nanopores based on an autoregressive latent variable model. We embed subsequences of DNA and introduce a conditional prior to address the challenge of a collapsing conditioning. We introduce an auxiliary regressor on the latent variable to encourage our model to learn an informative latent representation. We empirically demonstrate that our model achieves competitive simulation performance on experimental nanopore data. Moreover, we show we have learned an informative latent representation that is predictive of the DNA labels. We hypothesize that other biological factors of interest, beyond the DNA labels, can potentially be extracted from such a learned latent representation.

Graph Neural Networks for Carbon Dioxide Adsorption Prediction in Aluminium-Exchanged Zeolites

The ability to efficiently predict adsorption properties of zeolites can be of large benefit in accelerating the design process of novel materials. The existing configuration space for these materials is wide, while existing molecular simulation methods are computationally expensive. In this work, we propose a model which is 4 to 5 orders of magnitude faster at adsorption properties compared to molecular simulations. To validate the model, we generated datasets containing various aluminium configurations for the MOR, MFI, RHO and ITW zeolites along with their heat of adsorptions and Henry coefficients for CO$_2$, obtained from Monte Carlo simulations. The predictions obtained from the Machine Learning model are in agreement with the values obtained from the Monte Carlo simulations, confirming that the model can be used for property prediction. Furthermore, we show that the model can be used for identifying adsorption sites. Finally, we evaluate the capability of our model for generating novel zeolite configurations by using it in combination with a genetic algorithm.

Description Generation using Variational Auto-Encoders for precursor microRNA

Micro RNAs (miRNA) are a type of non-coding RNA, which are involved in gene regulation and can be associated with diseases such as cancer, cardiovascular and neurological diseases. As such, identifying the entire genome of miRNA can be of great relevance. Since experimental methods for novel precursor miRNA (pre-miRNA) detection are complex and expensive, computational detection using ML could be useful. Existing ML methods are often complex black boxes, which do not create an interpretable structural description of pre-miRNA. In this paper, we propose a novel framework, which makes use of generative modeling through Variational Auto-Encoders to uncover the generative factors of pre-miRNA. After training the VAE, the pre-miRNA description is developed using a decision tree on the lower dimensional latent space. Applying the framework to miRNA classification, we obtain a high reconstruction and classification performance, while also developing an accurate miRNA description.

Node classification in random trees

We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes (typically high dimensional embeddings). The tree topology is not predetermined and none of the label assignments are present during inference. Other methods that produce a distribution over node label assignment in trees (or more generally in graphs) either assume conditional independence of the label assignment, operate on a fixed graph topology, or require part of the node labels to be observed. Our method defines a Markov Network with the corresponding topology of the random tree and an associated Gibbs distribution. We parameterize the Gibbs distribution with a Graph Neural Network that operates on the random tree and the node embeddings. This allows us to estimate the likelihood of node assignments for a given random tree and use MCMC to sample from the distribution of node assignments. We evaluate our method on the tasks of node classification in trees on the Stanford Sentiment Treebank dataset. Our method outperforms the baselines on this dataset, demonstrating its effectiveness for modeling joint distributions of node labels in random trees.

KeyGen2Vec: Learning Document Embedding via Multi-label Keyword Generation in Question-Answering

Representing documents into high dimensional embedding space while preserving the structural similarity between document sources has been an ultimate goal for many works on text representation learning. Current embedding models, however, mainly rely on the availability of label supervision to increase the expressiveness of the resulting embeddings. In contrast, unsupervised embeddings are cheap, but they often cannot capture implicit structure in target corpus, particularly for samples that come from different distribution with the pretraining source. Our study aims to loosen up the dependency on label supervision by learning document embeddings via Sequence-to-Sequence (Seq2Seq) text generator. Specifically, we reformulate keyphrase generation task into multi-label keyword generation in community-based Question Answering (cQA). Our empirical results show that KeyGen2Vec in general is superior than multi-label keyword classifier by up to 14.7% based on Purity, Normalized Mutual Information (NMI), and F1-Score metrics. Interestingly, although in general the absolute advantage of learning embeddings through label supervision is highly positive across evaluation datasets, KeyGen2Vec is shown to be competitive with classifier that exploits topic label supervision in Yahoo! cQA with larger number of latent topic labels.

Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates

Managing divertor plasmas is crucial for operating reactor scale tokamak devices due to heat and particle flux constraints on the divertor target. Simulation is an important tool to understand and control these plasmas, however, for real-time applications or exhaustive parameter scans only simple approximations are currently fast enough. We address this lack of fast simulators using neural PDE surrogates, data-driven neural network-based surrogate models trained using solutions generated with a classical numerical method. The surrogate approximates a time-stepping operator that evolves the full spatial solution of a reference physics-based model over time. We use DIV1D, a 1D dynamic model of the divertor plasma, as reference model to generate data. DIV1D's domain covers a 1D heat flux tube from the X-point (upstream) to the target. We simulate a realistic TCV divertor plasma with dynamics induced by upstream density ramps and provide an exploratory outlook towards fast transients. State-of-the-art neural PDE surrogates are evaluated in a common framework and extended for properties of the DIV1D data. We evaluate (1) the speed-accuracy trade-off; (2) recreating non-linear behavior; (3) data efficiency; and (4) parameter inter- and extrapolation. Once trained, neural PDE surrogates can faithfully approximate DIV1D's divertor plasma dynamics at sub real-time computation speeds: In the proposed configuration, 2ms of plasma dynamics can be computed in $\approx$0.63ms of wall-clock time, several orders of magnitude faster than DIV1D.