Generative models are increasingly central to scientific workflows, yet their systematic use and interpretation require a proper understanding of their limitations through rigorous validation. Classic approaches struggle with scalability, statistical power, or interpretability when applied to high-dimensional data, making it difficult to certify the reliability of these models in realistic, high-dimensional scientific settings. Here, we propose the use of the New Physics Learning Machine (NPLM), a learning based approach to goodness-of-fit testing inspired by the Neyman-Pearson construction, to test generative networks trained on high-dimensional scientific data. We demonstrate the performance of NPLM for validation in two benchmark cases: generative models trained on mixtures of Gaussian models with increasing dimensionality, and a public end-to-end generator for the Large Hadron Collider called FlashSim, trained on jet data, typical in the field of high-energy physics. We demonstrate that the NPLM can serve as a powerful validation method while also providing a means to diagnose sub-optimally modeled regions of the data.

We propose a hybrid variational framework that enhances Neural Quantum States (NQS) with a Normalising Flow-based sampler to improve the expressivity and trainability of quantum many-body wavefunctions. Our approach decouples the sampling task from the variational ansatz by learning a continuous flow model that targets a discretised, amplitude-supported subspace of the Hilbert space. This overcomes limitations of Markov Chain Monte Carlo (MCMC) and autoregressive methods, especially in regimes with long-range correlations and volume-law entanglement. Applied to the transverse-field Ising model with both short- and long-range interactions, our method achieves comparable ground state energy errors with state-of-the-art matrix product states and lower energies than autoregressive NQS. For systems up to 50 spins, we demonstrate high accuracy and robust convergence across a wide range of coupling strengths, including regimes where competing methods fail. Our results showcase the utility of flow-assisted sampling as a scalable tool for quantum simulation and offer a new approach toward learning expressive quantum states in high-dimensional Hilbert spaces.

Recent years have witnessed a burgeoning interest in federated learning (FL). However, the contexts in which clients engage in sequential learning remain under-explored. Bridging FL and continual learning (CL) gives rise to a challenging practical problem: federated continual learning (FCL). Existing research in FCL primarily focuses on mitigating the catastrophic forgetting issue of continual learning while collaborating with other clients. We argue that the forgetting phenomena are not invariably detrimental. In this paper, we consider a more practical and challenging FCL setting characterized by potentially unrelated or even antagonistic data/tasks across different clients. In the FL scenario, statistical heterogeneity and data noise among clients may exhibit spurious correlations which result in biased feature learning. While existing CL strategies focus on a complete utilization of previous knowledge, we found that forgetting biased information is beneficial in our study. Therefore, we propose a new concept accurate forgetting (AF) and develop a novel generative-replay method~\method~which selectively utilizes previous knowledge in federated networks. We employ a probabilistic framework based on a normalizing flow model to quantify the credibility of previous knowledge. Comprehensive experiments affirm the superiority of our method over baselines.

The present study presents a novel application for normalizing flows for domain adaptation. The study investigates the ability of flow based neural networks to improve signal extraction of $\Lambda$ Hyperons at CLAS12. Normalizing Flows can help model complex probability density functions that describe physics processes, enabling uses such as event generation. $\Lambda$ signal extraction has been improved through the use of classifier networks, but differences in simulation and data domains limit classifier performance; this study utilizes the flows for domain adaptation between Monte Carlo simulation and data. We were successful in training a flow network to transform between the latent physics space and a normal distribution. We also found that applying the flows lessened the dependence of the figure of merit on the cut on the classifier output, meaning that there was a broader range where the cut results in a similar figure of merit.

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis Hastings algorithm have been extensively applied to get unbiased samples from target distributions. We systematically study central problems in conditional NFs, such as high variance, mode collapse and data efficiency. We propose adversarial training for NFs to ameliorate these problems. Experiments are conducted with low-dimensional synthetic datasets and XY spin models in two spatial dimensions.

The Exponential Mechanism (ExpM), a differentially private optimization method, promises many advantages over Differentially Private Stochastic Gradient Descent (DPSGD), the state-of-the-art (SOTA) and de facto method for differentially private machine learning (ML). Yet, ExpM has been historically stymied from differentially private training of modern ML algorithms by two obstructions: ExpM requires a sensitivity bound for the given loss function; ExpM requires sampling from a historically intractable density. We prove a sensitivity bound for $\ell(2)$ loss, and investigate using Normalizing Flows (NFs), deep networks furnishing approximate sampling from the otherwise intractable ExpM distribution. We prove that as the NF output converges to ExpM distribution, the privacy ($\varepsilon$) of an NF sample converges to that of the ExpM distribution. Under the assumption that the NF output distribution is the ExpM distribution, we empirically test ExpM+NF against DPSGD using the SOTA implementation (Opacus \cite{opacus} with PRV accounting) in multiple classification tasks on the Adult Dataset (census data) and MIMIC-III Dataset (healthcare records) using Logistic Regression and GRU-D, a deep learning recurrent neural network with \smallsim 20K-100K parameters. In all experiments we find ExpM+NF achieves greater than 94\% of the non-private training accuracy (AUC) with $\varepsilon$-DP for $\varepsilon$ a low as $1\mathrm{e}{-3}$ -- three orders of magnitude stronger privacy with similar accuracy. Further, performance results show ExpM+NF training time is comparable to (slightly less) than DPSGD. Limitations and future directions are provided; notably, research on NF approximation accuracy and its effect on privacy are a promising avenue to substantially advancing the field. Code for these experiments \hl{will be provided after review}.

A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this challenge and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as a series of quantitative experiments encompassing $10$ distinct test cases, which highlight NOFIS's superiority over baseline approaches.

High-precision modeling of systems is one of the main areas of industrial data analysis. Models of systems, their digital twins, are used to predict their behavior under various conditions. We have developed several models of a storage system using machine learning-based generative models. The system consists of several components: hard disk drive (HDD) and solid-state drive (SSD) storage pools with different RAID schemes and cache. Each storage component is represented by a probabilistic model that describes the probability distribution of the component performance in terms of IOPS and latency, depending on their configuration and external data load parameters. The results of the experiments demonstrate the errors of 4-10 % for IOPS and 3-16 % for latency predictions depending on the components and models of the system. The predictions show up to 0.99 Pearson correlation with Little's law, which can be used for unsupervised reliability checks of the models. In addition, we present novel data sets that can be used for benchmarking regression algorithms, conditional generative models, and uncertainty estimation methods in machine learning.

In this paper, we propose a self-supervised density estimation To develop a machine sound monitoring system, a method for detecting method using NF. Our method uses sound data from one machine ID anomalous sound is proposed. Exact likelihood estimation to detect anomalies (target data) and sound data from other machines using Normalizing Flows is a promising technique for unsupervised of the same machine type (outlier data), and the model is trained to anomaly detection, but it can fail at out-of-distribution detection assign higher likelihood to the target data and lower likelihood to since the likelihood is affected by the smoothness of the data. To improve the outlier data. This method is a self-supervised approach because the detection performance, we train the model to assign higher it improves the detection performance on one machine ID by introducing likelihood to target machine sounds and lower likelihood to sounds an auxiliary task in which the model discriminates the sound from other machines of the same machine type. We demonstrate that data of that machine ID (target data) from sound data of other machine this enables the model to incorporate a self-supervised classificationbased IDs with the same machine type (outlier data).