We present a data-efficient, multiscale framework for predicting the density profiles of confined fluids at the nanoscale. While accurate density estimates require prohibitively long timescales that are inaccessible by ab initio molecular dynamics (AIMD) simulations, machine-learned molecular dynamics (MLMD) offers a scalable alternative, enabling the generation of force predictions at ab initio accuracy with reduced computational cost. However, despite their efficiency, MLMD simulations remain constrained by femtosecond timesteps, which limit their practicality for computing long-time averages needed for accurate density estimation. To address this, we propose a conditional denoising diffusion probabilistic model (DDPM) based quasi-continuum approach that predicts the long-time behavior of force profiles along the confinement direction, conditioned on noisy forces extracted from a limited AIMD dataset. The predicted smooth forces are then linked to continuum theory via the Nernst-Planck equation to reveal the underlying density behavior. We test the framework on water confined between two graphene nanoscale slits and demonstrate that density profiles for channel widths outside of the training domain can be recovered with ab initio accuracy. Compared to AIMD and MLMD simulations, our method achieves orders-of-magnitude speed-up in runtime and requires significantly less training data than prior works.

We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on with the observables of a quantum reservoir implementable with interacting Rydberg atoms. Training and test data of the fermionic system are generated using a Density Functional Theory approach. We test the performance of the method for several Hamiltonian parameters, finding a general common behavior of the error as a function of measurement time. At sufficiently large measurement times, we find that the method outperforms the classical linear kernel method and can be competitive with the radial basis function method.

The kinematics of stars in dwarf spheroidal galaxies have been studied to understand the structure of dark matter halos. However, the kinematic information of these stars is often limited to celestial positions and line-of-sight velocities, making full phase space analysis challenging. Conventional methods rely on projected analytic phase space density models with several parameters and infer dark matter halo structures by solving the spherical Jeans equation. In this paper, we introduce an unsupervised machine learning method for solving the spherical Jeans equation in a model-independent way as a first step toward model-independent analysis of dwarf spheroidal galaxies. Using equivariant continuous normalizing flows, we demonstrate that spherically symmetric stellar phase space densities and velocity dispersions can be estimated without model assumptions. As a proof of concept, we apply our method to Gaia challenge datasets for spherical models and measure dark matter mass densities for given velocity anisotropy profiles. Our method can identify halo structures accurately, even with a small number of tracer stars.

Knowledge about the internal physical structure of stars is crucial to understanding their evolution. The novel binary population synthesis code POSYDON includes a module for interpolating the stellar and binary properties of any system at the end of binary MESA evolution based on a pre-computed set of models. In this work, we present a new emulation method for predicting stellar profiles, i.e., the internal stellar structure along the radial axis, using machine learning techniques. We use principal component analysis for dimensionality reduction and fully-connected feed-forward neural networks for making predictions. We find accuracy to be comparable to that of nearest neighbor approximation, with a strong advantage in terms of memory and storage efficiency. By delivering more information about the evolution of stellar internal structure, these emulators will enable faster simulations of higher physical fidelity with large-scale simulations of binary star population synthesis possible with POSYDON and other population synthesis codes.

Message passing neural networks (MPNNs) [18-learn from reference quantum mechanical calculations 21] employ a number of graph convolution layers to communicate and then predict the energy and forces of atomic configurations information between atoms, thereby capturing quickly, thus allowing for a more accurate long-range interaction up to the local cutoff radius times and comprehensive exploration of material and molecular the number of layers. However, if parts of the system are properties at scale [1, 2]. Most state-of-the-art MLIP disconnected on the graph, e.g. two molecules with a distance methods use a short-range approximation: the effective beyond the cutoff, the message passing scheme does potential energy surface experienced by one atom is determined not help. A very interesting approach is the long-distance by its atomic neighborhood.

Recent years have seen a significant increase in the use of machine intelligence for predicting electronic structure, molecular force fields, and the physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging on recent advancements of functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability and computational efficiency, enabling their broader applications across diverse materials and chemical systems.

This work presents a deep-learning approach to estimate atmospheric density profiles for use in planetary entry guidance problems. A long short-term memory (LSTM) neural network is trained to learn the mapping between measurements available onboard an entry vehicle and the density profile through which it is flying. Measurements include the spherical state representation, Cartesian sensed acceleration components, and a surface-pressure measurement. Training data for the network is initially generated by performing a Monte Carlo analysis of an entry mission at Mars using the fully numerical predictor-corrector guidance (FNPEG) algorithm that utilizes an exponential density model, while the truth density profiles are sampled from MarsGRAM. A curriculum learning procedure is developed to refine the LSTM network's predictions for integration within the FNPEG algorithm. The trained LSTM is capable of both predicting the density profile through which the vehicle will fly and reconstructing the density profile through which it has already flown. The performance of the FNPEG algorithm is assessed for three different density estimation techniques: an exponential model, an exponential model augmented with a first-order fading-memory filter, and the LSTM network. Results demonstrate that using the LSTM model results in superior terminal accuracy compared to the other two techniques when considering both noisy and noiseless measurements.

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity.

The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) are based on the accurate estimations of plasma density and plasma temperature. The conventional methods for electron density measurements offer axial and radial profiles for any given linear LTP device. These methods have major disadvantages of operational range (not very wide), cumbersome instrumentation, and complicated data analysis procedures. The article proposes a Deep Learning (DL) assisted microwave-plasma interaction-based non-invasive strategy, which can be used as a new alternative approach to address some of the challenges associated with existing plasma density measurement techniques. The electric field pattern due to microwave scattering from plasma is utilized to estimate the density profile. The proof of concept is tested for a simulated training data set comprising a low-temperature, unmagnetized, collisional plasma. Different types of symmetric (Gaussian-shaped) and asymmetrical density profiles, in the range $10^{16}-10^{19}$ m$^{-3}$, addressing a range of experimental configurations have been considered in our study. Real-life experimental issues such as the presence of noise and the amount of measured data (dense vs sparse) have been taken into consideration while preparing the synthetic training data-sets. The DL-based technique has the capability to determine the electron density profile within the plasma. The performance of the proposed deep learning-based approach has been evaluated using three metrics- SSIM, RMSLE, and MAPE. The obtained results show promising performance in estimating the 2D radial profile of the density for the given linear plasma device and affirms the potential of the proposed ML-based approach in plasma diagnostics.