Crystal property prediction is a crucial aspect of developing novel materials. However, there are two technical challenges to be addressed for speeding up the investigation of crystals. First, labeling crystal properties is intrinsically difficult due to the high cost and time involved in physical simulations or lab experiments. Second, crystals adhere to a specific quantum chemical principle known as periodic invariance, which is often not captured by existing machine learning methods. To overcome these challenges, we propose the crystal-specific pre-training framework for learning crystal representations with self-supervision. The framework designs a mutex mask strategy for enhancing representation learning so as to alleviate the limited labels available for crystal property prediction. Moreover, we take into account the specific periodic invariance in crystal structures by developing a periodic invariance multi-graph module and periodic attribute learning within our framework. This framework has been tested on eight different tasks. The experimental results on these tasks show that the framework achieves promising prediction performance and is able to outperform recent strong baselines.

Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of minor industrial relevance. This paper demonstrates the development of a novel deep learning framework for real-time predictions of the impact of manufacturing and build variations on the overall performance of axial compressors in gas turbines, with a focus on tip clearance variations. The associated scatter in efficiency can significantly increase the $CO_2$ emissions, thus being of great industrial and environmental relevance. The proposed \textit{C(NN)FD} architecture achieves in real-time accuracy comparable to the CFD benchmark. Predicting the flow field and using it to calculate the corresponding overall performance renders the methodology generalisable, while filtering only relevant parts of the CFD solution makes the methodology scalable to industrial applications.

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desired. In absence of the governing equations describing the dynamics, we need to construct the parametric reduced-order surrogate model in a non-intrusive fashion. In this setting, the usual residual-based error estimate for optimal parameter sampling associated with the reduced basis method is not directly available. Our work provides a non-intrusive optimality criterion to efficiently populate the parameter snapshots, thereby, enabling us to effectively construct a parametric surrogate model. We consider separate parameter-specific proper orthogonal decomposition (POD) subspaces and propose an active-learning-driven surrogate model using kernel-based shallow neural networks, abbreviated as ActLearn-POD-KSNN surrogate model. To demonstrate the validity of our proposed ideas, we present numerical experiments using two physical models, namely Burgers' equation and shallow water equations. Both the models have mixed -- convective and diffusive -- effects within their respective parameter domains, with each of them dominating in certain regions. The proposed ActLearn-POD-KSNN surrogate model efficiently predicts the solution at new parameter locations, even for a setting with multiple interacting shock profiles.

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithm termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization-based EpsMix algorithm is also proposed and shown to achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

Machine Learning models have emerged as a powerful tool for fast and accurate prediction of different crystalline properties. Exiting state-of-the-art models rely on a single modality of crystal data i.e. crystal graph structure, where they construct multi-graph by establishing edges between nearby atoms in 3D space and apply GNN to learn materials representation. Thereby, they encode local chemical semantics around the atoms successfully but fail to capture important global periodic structural information like space group number, crystal symmetry, rotational information, etc, which influence different crystal properties. In this work, we leverage textual descriptions of materials to model global structural information into graph structure and learn a more robust and enriched representation of crystalline materials. To this effect, we first curate a textual dataset for crystalline material databases containing descriptions of each material. Further, we propose CrysMMNet, a simple multi-modal framework, which fuses both structural and textual representation together to generate a joint multimodal representation of crystalline materials. We conduct extensive experiments on two benchmark datasets across ten different properties to show that CrysMMNet outperforms existing state-of-the-art baseline methods with a good margin. We also observe that fusing the textual representation with crystal graph structure provides consistent improvement for all the SOTA GNN models compared to their own vanilla versions. We have shared the textual dataset, that we have curated for both the benchmark material databases, with the community for future use.

It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes. Key to a practical success of the approach is the identification of a set of observables which form a good basis in which to expand the slow relaxation modes. Good observables are, however, difficult to identify {\em a priori} and sub-optimal choices can lead to significant underestimations of characteristic timescales. Leveraging the representation of slow dynamics in terms of Hidden Markov Model (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. We apply the approach to an analytically solvable model system, as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of the Koopman operators and correctly identify key states and transition timescales of stochastic systems, even when good observables are not known {\em a priori}.

Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random walk model in NetLogo, a leading platform for computational thinking, eco-system thinking, and multi-agent cross-platform programming environment. The deterministic random walk is foundational to modeling dynamical processes on complex networks. Inspired by the temporal visualizations offered in NetLogo, we investigated the relationship between network topology and diffusion saturation time for the deterministic random walk model. Our analysis uncovers that in Erd\H{o}s-R\'{e}nyi graphs, the saturation time exhibits an asymmetric pattern with a considerable probability of occurrence. This behavior occurs when the hubs, defined as nodes with relatively higher number of connections, emerge in Erd\H{o}s-R\'{e}nyi graphs. Yet, our analysis yields that the hubs in Barab\'{a}si-Albert model stabilize the the convergence time of the deterministic random walk model. These findings strongly suggest that depending on the dynamical process running on complex networks, complementing characteristics other than the degree need to be taken into account for considering a node as a hub. We have made our development open-source, available to the public at no cost at https://github.com/bravandi/NetLogo-Dynamical-Processes.

The increasing installation rate of wind power poses great challenges to the global power system. In order to ensure the reliable operation of the power system, it is necessary to accurately forecast the wind speed and power of the wind turbines. At present, deep learning is progressively applied to the wind speed prediction. Nevertheless, the recent deep learning methods still reflect the embarrassment for practical applications due to model interpretability and hardware limitation. To this end, a novel deep knowledge-based learning method is proposed in this paper. The proposed method hybridizes pre-training method and auto-encoder structure to improve data representation and modeling of the deep knowledge-based learning framework. In order to form knowledge and corresponding absorbers, the original data is preprocessed by an optimization model based on correlation to construct multi-layer networks (knowledge) which are absorbed by sequence to sequence (Seq2Seq) models. Specifically, new cognition and memory units (CMU) are designed to reinforce traditional deep learning framework. Finally, the effectiveness of the proposed method is verified by three wind prediction cases from a wind farm in Liaoning, China. Experimental results show that the proposed method increases the stability and training efficiency compared to the traditional LSTM method and LSTM/GRU-based Seq2Seq method for applications of wind speed forecasting.

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation, such as partial differential equations with different parameters or different initial conditions. The network consists of two sub-networks, the Branch net and the Trunk net. For an objective operator G, the Branch net encodes different input functions u at the same number of sensors, and the Trunk net evaluates the output function at any location. By minimizing the error between the evaluated output q and the expected output G(u)(y), DeepONet generates a good approximation of the operator G. In order to preserve essential physical properties of PDEs, such as the Energy Dissipation Law, we adopt a scalar auxiliary variable approach to generate the minimization problem. It introduces a modified energy and enables unconditional energy dissipation law at the discrete level. By taking the parameter as a function of time t, this network can predict the accurate solution at any further time with feeding data only at the initial state. The data needed can be generated by the initial conditions, which are readily available. In order to validate the accuracy and efficiency of our neural networks, we provide numerical simulations of several partial differential equations, including heat equations, parametric heat equations and Allen-Cahn equations.

Urban land use structures impact local climate conditions of metropolitan areas. To shed light on the mechanism of local climate wrt. urban land use, we present a novel, data-driven deep learning architecture and pipeline, DeepLCZChange, to correlate airborne LiDAR data statistics with the Landsat 8 satellite's surface temperature product. A proof-of-concept numerical experiment utilizes corresponding remote sensing data for the city of New York to verify the cooling effect of urban forests.