Molecular dynamics simulations are crucial for understanding complex physical, chemical, and biological processes at the atomic level. However, accurately capturing interactions across multiple spatial and temporal scales remains a significant challenge. We present a novel framework that jointly models spatial and temporal multiscale interactions in molecular dynamics. Our approach leverages Graph Fourier Transforms to decompose molecular structures into different spatial scales and employs Neural Ordinary Differential Equations to model the temporal dynamics in a curated manner influenced by the spatial modes. We evaluate our model on the MD17 dataset, demonstrating consistent performance improvements over state-of-the-art baselines across multiple molecules, particularly under challenging conditions such as irregular timestep sampling and long-term prediction horizons. Ablation studies confirm the significant contributions of both spatial and temporal multiscale modeling components.

In this paper a streaming weak-SINDy algorithm is developed specifically for compressing streaming scientific data. The production of scientific data, either via simulation or experiments, is undergoing an stage of exponential growth, which makes data compression important and often necessary for storing and utilizing large scientific data sets. As opposed to classical "offline" compression algorithms that perform compression on a readily available data set, streaming compression algorithms compress data "online" while the data generated from simulation or experiments is still flowing through the system. This feature makes streaming compression algorithms well-suited for scientific data compression, where storing the full data set offline is often infeasible. This work proposes a new streaming compression algorithm, streaming weak-SINDy, which takes advantage of the underlying data characteristics during compression. The streaming weak-SINDy algorithm constructs feature matrices and target vectors in the online stage via a streaming integration method in a memory efficient manner. The feature matrices and target vectors are then used in the offline stage to build a model through a regression process that aims to recover equations that govern the evolution of the data. For compressing high-dimensional streaming data, we adopt a streaming proper orthogonal decomposition (POD) process to reduce the data dimension and then use the streaming weak-SINDy algorithm to compress the temporal data of the POD expansion. We propose modifications to the streaming weak-SINDy algorithm to accommodate the dynamically updated POD basis. By combining the built model from the streaming weak-SINDy algorithm and a small amount of data samples, the full data flow could be reconstructed accurately at a low memory cost, as shown in the numerical tests.

Variational autoencoder (VAE) architectures have the potential to develop reduced-order models (ROMs) for chaotic fluid flows. We propose a method for learning compact and near-orthogonal ROMs using a combination of a $\beta$-VAE and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The $\beta$-VAE is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent space. Using the $\beta$-VAE to learn disentangled representations in latent-space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincar\'e maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal data representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of modeling spatiotemporal data and characterizing spatial/temporal patterns with the proposed model. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/vars.

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

When photons are used as the carriers of quantum information to transmit data, that information is often distorted due to environment fluctuations destroying the fragile quantum states necessary to preserve it. Researchers from Louisiana State University exploited a type of machine learning to correct for information distortion in quantum systems composed of photons. Published in Advanced Quantum Technologies, the team demonstrated that machine learning techniques using the self-learning and self-evolving features of artificial neural networks can help correct distorted information. This results outperformed traditional protocols that rely on conventional adaptive optics. "We are still in the fairly early stages of understanding the potential for machine learning techniques to play a role in quantum information science," said Dr. Sara Gamble, program manager at the Army Research Office, an element of U.S. Army Combat Capabilities Development Command, known as DEVCOM, Army Research Laboratory.

When photons are used as the carriers of quantum information to transmit data, that information is often distorted due to environment fluctuations destroying the fragile quantum states necessary to preserve it. Researchers from Louisiana State University exploited a type of machine learning to correct for information distortion in quantum systems composed of photons. Published in Advanced Quantum Technologies, the team demonstrated that machine learning techniques using the self-learning and self-evolving features of artificial neural networks can help correct distorted information. This results outperformed traditional protocols that rely on conventional adaptive optics. "We are still in the fairly early stages of understanding the potential for machine learning techniques to play a role in quantum information science," said Dr. Sara Gamble, program manager at the Army Research Office, an element of U.S. Army Combat Capabilities Development Command, known as DEVCOM, Army Research Laboratory.

We present a new method for multi-modal, long-term vehicle trajectory prediction. Our approach relies on using lane centerlines captured in rich maps of the environment to generate a set of proposed goal paths for each vehicle. Using these paths -- which are generated at run time and therefore dynamically adapt to the scene -- as spatial anchors, we predict a set of goal-based trajectories along with a categorical distribution over the goals. This approach allows us to directly model the goal-directed behavior of traffic actors, which unlocks the potential for more accurate long-term prediction. Our experimental results on both a large-scale internal driving dataset and on the public nuScenes dataset show that our model outperforms state-of-the-art approaches for vehicle trajectory prediction over a 6-second horizon. We also empirically demonstrate that our model is better able to generalize to road scenes from a completely new city than existing methods.

This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability matrix and a state sequence that minimizes the prediction error for the state-space model. Moreover, we observe that DMD seeks to solve a rank-constrained matrix regression problem that minimizes the prediction error of an extended autoregressive model. We prove that existence conditions for perfect (error-free) state-space and low-rank extended autoregressive models are equivalent and that the SID and DMD optimization problems are equivalent. We exploit these results to propose a SID-DMD algorithm that delivers a provably optimal model and that is easy to implement. We demonstrate our developments using a case study that aims to build dynamical models directly from video data.

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized by a potentially different system matrix, and we model this stack of system matrices as a low rank tensor. Because of its structure, the model is scalable to high-dimensional data and can easily incorporate priors such as smoothness over time. We find the components of the tensor using alternating minimization and prove that any stationary point of this algorithm is a local minimum. In a test case, our method identifies the true rank of a switching linear system in the presence of noise. We illustrate our model's utility and superior scalability over extant methods when applied to several synthetic and real examples, including a nonlinear dynamical system, worm behavior, sea surface temperature, and monkey brain recordings.