arXiv subjects

Lorenzo Zanisi

Publications and source records attributed to Lorenzo Zanisi.

At least 19 recordsLinked to original sources

arXiv2026

GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to viable fusion power is understanding plasma turbulence, which significantly impairs plasma confinement, and is vital for next-generation reactor design. Plasma turbulence is governed by the nonlinear gyrokinetic equation, which evolves a 5D distribution function over time. Due to its high computational cost, reduced-order models are often employed in practice to approximate turbulent transport of energy. However, they omit nonlinear effects unique to the full 5D dynamics. To tackle this, we introduce GyroSwin, the first scalable 5D neural surrogate that can model 5D nonlinear gyrokinetic simulations, thereby capturing the physical phenomena neglected by reduced models, while providing accurate estimates of turbulent heat transport. GyroSwin (i) extends hierarchical Vision Transformers to 5D, (ii) introduces cross-attention and integration modules for latent 3D$\leftrightarrow$5D interactions between electrostatic potential fields and the distribution function, and (iii) performs channelwise mode separation inspired by nonlinear physics. We demonstrate that GyroSwin outperforms widely used reduced numerics on heat flux prediction, captures the turbulent energy cascade, and reduces the cost of fully resolved nonlinear gyrokinetics by three orders of magnitude while remaining physically verifiable. GyroSwin shows promising scaling laws, tested up to one billion parameters, paving the way for scalable neural surrogates for gyrokinetic simulations of plasma turbulence.

physics.plasm-ph↗

arXiv2026

A Shortcut to Statistically Steady-State Turbulence with Flow Matching

Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.

physics.plasm-ph↗

arXiv2026

Data-Efficient Neural Operator Training via Physics-Based Active Learning

Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively acquiring the most informative samples in an iterative manner. We introduce physics-based acquisition - a novel physics-informed active learning algorithm that leverages the partial differential equation residual to guide data selection. We validate the method by presenting numerical experiments for the 1D Burgers equation and the 2D compressible Navier-Stokes equations. We show that, in our experiments, physics-based acquisition consistently outperforms random acquisition and matches the state of the art in data efficiency. At the same time, it has the unique advantage of injecting a physics inductive bias into the training process, ensuring that simulation cost is spent where the model's physical understanding is weakest.

cs.LG↗

arXiv2026

Learning Physical Operators using Neural Operators

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addresses these limitations by decomposing PDEs using operator splitting methods, training separate neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions. This modular mixture-of-experts architecture enables generalisation to novel physical regimes by explicitly encoding the underlying operator structure. We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side, enabling continuous-in-time predictions through standard ODE solvers and implicitly enforcing PDE constraints. Demonstrated on incompressible and compressible Navier--Stokes equations, our approach achieves better convergence and superior performance when generalising to unseen physics. The method remains parameter-efficient, enabling temporal extrapolation beyond training horizons, and provides interpretable components whose behaviour can be verified against known physics.

cs.LG↗

arXiv2026

Physics-Informed Neural Compression of High-Dimensional Plasma Data

High-fidelity scientific simulations are now producing unprecedented amounts of data, creating a storage and analysis bottleneck. A single simulation can generate tremendous data volumes, often forcing researchers to discard valuable information. A prime example of this is plasma turbulence described by the gyrokinetic equations: nonlinear, multiscale, and 5D in phase space. It constitutes one of the most computationally demanding frontiers of modern science, with runs taking weeks and yielding tens of terabytes of data dumps. The increasing storage demands underscore the importance of compression. However, reconstructed snapshots do not necessarily preserve essential physical quantities. We present a spatiotemporal evaluation pipeline, accounting for structural phenomena and multi-scale transient fluctuations to assess the degree of physical fidelity. Indeed, we find that various compression techniques lack preservation of both spatial mode structure and temporal turbulence characteristics. Therefore, we explore Physics-Informed Neural Compression (PINC), which incorporates physics-informed losses tailored to gyrokinetics and enables extreme compressions ratios of over 70,000x. Entropy coding on top of PINC further pushes it to 120,000x. This direction provides a viable and scalable solution to the prohibitive storage demands of gyrokinetics, enabling post-hoc analyses that were previously infeasible.

physics.plasm-ph↗

arXiv2026

Uncertainty Quantification of Surrogate Models using Conformal Prediction

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide uncertainty estimates, they offer no statistical guarantees and struggle with high-dimensional spatio-temporal problems due to computational costs. We present a conformal prediction (CP) framework that provides statistically guaranteed marginal coverage for surrogate models in a model-agnostic manner with near-zero computational cost. Our approach handles high-dimensional spatio-temporal outputs by performing cell-wise calibration while preserving the tensorial structure of predictions. Through extensive empirical evaluation across diverse applications including fluid dynamics, magnetohydrodynamics, weather forecasting, and fusion diagnostics, we demonstrate that CP achieves empirical coverage with valid error bars regardless of model architecture, training regime, or output dimensionality. We evaluate three nonconformity scores (conformalised quantile regression, absolute error residual, and standard deviation) for both deterministic and probabilistic models, showing that guaranteed coverage holds even for out-of-distribution predictions where models are deployed on physics regimes different from training data. Calibration requires only seconds to minutes on standard hardware. The framework enables rigorous validation of pre-trained surrogate models for downstream applications without retraining. While CP provides marginal rather than conditional coverage and assumes exchangeability between calibration and test data, our method circumvents the curse of dimensionality inherent in traditional uncertainty quantification approaches, offering a practical tool for trustworthy deployment of machine learning in physical sciences.

cs.AI↗

arXiv2025

Efficient dataset construction using active learning and uncertainty-aware neural networks for plasma turbulent transport surrogate models

This work demonstrates a proof-of-principle for using uncertainty-aware architectures, in combination with active learning techniques and an in-the-loop physics simulation code as a data labeller, to construct efficient datasets for data-driven surrogate model generation. Building off of a previous proof-of-principle successfully demonstrating training set reduction on static pre-labelled datasets, using the ADEPT framework, this strategy was applied again to the plasma turbulent transport problem within tokamak fusion plasmas, specifically the QuaLiKiz quasilinear electrostatic gyrokinetic turbulent transport code. While QuaLiKiz provides relatively fast evaluations, this study specifically targeted small datasets to serve as a proxy for more expensive codes, such as CGYRO or GENE. The newly implemented algorithm uses the SNGP architecture for the classification component of the problem and the BNN-NCP architecture for the regression component, training models for all turbulent modes (ITG, TEM, ETG) and all transport fluxes ($Q_e$, $Q_i$, $Γ_e$, $Γ_i$, and $Π_i$) described by the general QuaLiKiz output. With 45 active learning iterations, moving from a small initial training set of $10^{2}$ to a final set of $10^{4}$, the resulting models reached a $F_1$ classification performance of ~0.8 and a $R^2$ regression performance of ~0.75 on an independent test set across all outputs. This extrapolates to reaching the same performance and efficiency as the previous ADEPT pipeline, although on a problem with 1 extra input dimension. While the improvement rate achieved in this implementation diminishes faster than expected, the overall technique is formulated with components that can be upgraded and generalized to many surrogate modeling applications beyond plasma turbulent transport predictions.

physics.plasm-ph↗

arXiv2025

Calibrated Physics-Informed Uncertainty Quantification

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

cs.LG↗

arXiv2025

5D Neural Surrogates for Nonlinear Gyrokinetic Simulations of Plasma Turbulence

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma confinement. Modelling turbulence is crucial to design performing plasma scenarios for next-generation reactor-class devices and current experimental machines. The nonlinear gyrokinetic equation underpinning turbulence modelling evolves a 5D distribution function over time. Solving this equation numerically is extremely expensive, requiring up to weeks for a single run to converge, making it unfeasible for iterative optimisation and control studies. In this work, we propose a method for training neural surrogates for 5D gyrokinetic simulations. Our method extends a hierarchical vision transformer to five dimensions and is trained on the 5D distribution function for the adiabatic electron approximation. We demonstrate that our model can accurately infer downstream physical quantities such as heat flux time trace and electrostatic potentials for single-step predictions two orders of magnitude faster than numerical codes. Our work paves the way towards neural surrogates for plasma turbulence simulations to accelerate deployment of commercial energy production via nuclear fusion.

physics.plasm-ph↗

arXiv2024

Valid Error Bars for Neural Weather Models using Conformal Prediction

Neural weather models have shown immense potential as inexpensive and accurate alternatives to physics-based models. However, most models trained to perform weather forecasting do not quantify the uncertainty associated with their forecasts. This limits the trust in the model and the usefulness of the forecasts. In this work we construct and formalise a conformal prediction framework as a post-processing method for estimating this uncertainty. The method is model-agnostic and gives calibrated error bounds for all variables, lead times and spatial locations. No modifications are required to the model and the computational cost is negligible compared to model training. We demonstrate the usefulness of the conformal prediction framework on a limited area neural weather model for the Nordic region. We further explore the advantages of the framework for deterministic and probabilistic models.

cs.LG↗

arXiv2024

Plasma Surrogate Modelling using Fourier Neural Operators

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (MSE in the normalised domain $\approx$ $10^{-5}$). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations (PDE), and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e., cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

physics.plasm-ph↗

arXiv2023

Fourier-RNNs for Modelling Noisy Physics Data

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required temporal dependencies. However, most existing sequential models operate within finite-dimensional Euclidean spaces which offer limited functionality when employed in modelling physics relevant data. Alternatively recent work with neural operator learning within the Fourier space has shown efficient strategies for parameterising Partial Differential Equations (PDE). In this work, we propose a novel sequential model, built to handle Physics relevant data by way of amalgamating the conventional RNN architecture with that of the Fourier Neural Operators (FNO). The Fourier-RNN allows for learning the mappings from the input to the output as well as to the hidden state within the Fourier space associated with the temporal data. While the Fourier-RNN performs identical to the FNO when handling PDE data, it outperforms the FNO and the conventional RNN when deployed in modelling noisy, non-Markovian data.

cs.LG↗

arXiv2023

Fourier Neural Operator for Plasma Modelling

Predicting plasma evolution within a Tokamak is crucial to building a sustainable fusion reactor. Whether in the simulation space or within the experimental domain, the capability to forecast the spatio-temporal evolution of plasma field variables rapidly and accurately could improve active control methods on current tokamak devices and future fusion reactors. In this work, we demonstrate the utility of using Fourier Neural Operator (FNO) to model the plasma evolution in simulations and experiments. Our work shows that the FNO is capable of predicting magnetohydrodynamic models governing the plasma dynamics, 6 orders of magnitude faster than the traditional numerical solver, while maintaining considerable accuracy (NMSE $\sim 10^{-5})$. Our work also benchmarks the performance of the FNO against other standard surrogate models such as Conv-LSTM and U-Net and demonstrate that the FNO takes significantly less time to train, requires less parameters and outperforms other models. We extend the FNO approach to model the plasma evolution observed by the cameras positioned within the MAST spherical tokamak. We illustrate its capability in forecasting the formation of filaments within the plasma as well as the heat deposits. The FNO deployed to model the camera is capable of forecasting the full length of the plasma shot within half the time of the shot duration.

physics.plasm-ph↗

arXiv2022

Testing the key role of the stellar mass-halo mass relation in galaxy merger rates and morphologies via DECODE, a novel Discrete statistical sEmi-empiriCal mODEl

The relative roles of mergers and star formation in regulating galaxy growth are still a matter of intense debate. We here present our DECODE, a new Discrete statistical sEmi-empiriCal mODEl specifically designed to predict rapidly and efficiently, in a full cosmological context, galaxy assembly and merger histories for any given input stellar mass-halo mass (SMHM) relation. DECODE generates object-by-object dark matter merger trees (hence discrete) from accurate subhalo mass and infall redshift probability functions (hence statistical) for all subhaloes, including those residing within other subhaloes, with virtually no resolution limits on mass or volume. Merger trees are then converted into galaxy assembly histories via an input, redshift dependent SMHM relation, which is highly sensitive to the significant systematics in the galaxy stellar mass function and on its evolution with cosmic time. DECODE can accurately reproduce the predicted mean galaxy merger rates and assembly histories of hydrodynamic simulations and semi-analytic models, when adopting in input their SMHM relations. In the present work we use DECODE to prove that only SMHM relations implied by stellar mass functions characterized by large abundances of massive galaxies and significant redshift evolution, at least at $M_\star \gtrsim 10^{11} \, M_\odot$, can simultaneously reproduce the local abundances of satellite galaxies, the galaxy (major merger) pairs since $z \sim 3$, and the growth of Brightest Cluster Galaxies. The same models can also reproduce the local fraction of elliptical galaxies, on the assumption that these are strictly formed by major mergers, but not the full bulge-to-disc ratio distributions, which require additional processes.

astro-ph.CO↗

arXiv2021

The size function of massive satellites from the $R_e-R_h$ and $M_{star}-M_h$ relations: constraining the role of environment

In previous work we showed that a semi-empirical model in which galaxies in host dark matter haloes are assigned stellar masses via a stellar mass-halo mass (SMHM) relation and sizes ($R_e$) via a linear and tight $R_e-R_h$ relation, can faithfully reproduce the size function of local SDSS central galaxies and the strong size evolution of massive galaxies (MGs, $M_{\rm star}>10^{11.2}M_\odot$). In this third paper of the series, we focus on the population of satellite MGs. We find that without any additional calibration and irrespective of the exact SMHM relation, fraction of quenched galaxies or level of stellar stripping, the same model is able to reproduce the local size function of quiescent satellite MGs in SDSS. In addition, the same model can reproduce the puzzling weak dependence of mean size on host halo mass for both central and satellite galaxies. The model also matches the size function of starforming satellite MGs, after assuming that some of them transform into massive lenticulars in a few Gyr after infalling in the group/cluster environment. However, the vast majority of satellite lenticulars is predicted to form before infall. The $R_e-R_h$ appears to be fundamental to connect galaxies and their host haloes.

astro-ph.GA↗

arXiv2020

The relationship between fine galaxy stellar morphology and star formation activity in cosmological simulations: a deep learning view

Hydrodynamical simulations of galaxy formation and evolution attempt to fully model the physics that shapes galaxies. The agreement between the morphology of simulated and real galaxies, and the way the morphological types are distributed across galaxy scaling relations are important probes of our knowledge of galaxy formation physics. Here we propose an unsupervised deep learning approach to perform a stringent test of the fine morphological structure of galaxies coming from the Illustris and IllustrisTNG (TNG100 and TNG50) simulations against observations from a subsample of the Sloan Digital Sky Survey. Our framework is based on PixelCNN, an autoregressive model for image generation with an explicit likelihood. We adopt a strategy that combines the output of two PixelCNN networks in a metric that isolates the fine morphological details of galaxies from the sky background. We are able to \emph{quantitatively} identify the improvements of IllustrisTNG, particularly in the high-resolution TNG50 run, over the original Illustris. However, we find that the fine details of galaxy structure are still different between observed and simulated galaxies. This difference is driven by small, more spheroidal, and quenched galaxies which are globally less accurate regardless of resolution and which have experienced little improvement between the three simulations explored. We speculate that this disagreement, that is less severe for quenched disky galaxies, may stem from a still too coarse numerical resolution, which struggles to properly capture the inner, dense regions of quenched spheroidal galaxies.

astro-ph.GA↗

arXiv2019

Probing black hole accretion tracks, scaling relations and radiative efficiencies from stacked X-ray active galactic nuclei

The masses of supermassive black holes at the centres of local galaxies appear to be tightly correlated with the mass and velocity dispersions of their galactic hosts. However, the local Mbh-Mstar relation inferred from dynamically measured inactive black holes is up to an order-of-magnitude higher than some estimates from active black holes, and recent work suggests that this discrepancy arises from selection bias on the sample of dynamical black hole mass measurements. In this work we combine X-ray measurements of the mean black hole accretion luminosity as a function of stellar mass and redshift with empirical models of galaxy stellar mass growth, integrating over time to predict the evolving Mbh-Mstar relation. The implied relation is nearly independent of redshift, indicating that stellar and black hole masses grow, on average, at similar rates. Matching the de-biased local Mbh-Mstar relation requires a mean radiative efficiency ~0.15, in line with theoretical expectations for accretion onto spinning black holes. However, matching the "raw" observed relation for inactive black holes requires a mean radiative efficiency around 0.02, far below theoretical expectations. This result provides independent evidence for selection bias in dynamically estimated black hole masses, a conclusion that is robust to uncertainties in bolometric corrections, obscured active black hole fractions, and kinetic accretion efficiency. For our fiducial assumptions, they favour moderate-to-rapid spins of typical supermassive black holes, to achieve a mean radiative efficiency ~0.12-0.20. Our approach has similarities to the classic Soltan analysis, but by using galaxy-based data instead of integrated quantities we are able to focus on regimes where observational uncertainties are minimized.

astro-ph.GA↗

arXiv2019

Galaxy sizes and the galaxy-halo connection -- I: the remarkable tightness of the size distributions

The mass and structural assembly of galaxies is a matter of intense debate. Current theoretical models predict the existence of a linear relationship between galaxy size ($R_e$) and the host dark matter halo virial radius ($R_h$).\\ By making use of semi-empirical models compared to the size distributions of central galaxies from the Sloan Digital Sky Survey, we provide robust constraints on the normalization and scatter of the $R_e-R_h$ relation. We explore the parameter space of models in which the $R_e-R_h$ relation is mediated by either the spin parameter or the concentration of the host halo, or a simple constant the nature of which is in principle unknown. We find that the data require extremely tight relations for both early-type and late-type galaxies (ETGs,LTGs), especially for more massive galaxies. These constraints challenge models based solely on angular momentum conservation, which predict significantly wider distributions of galaxy sizes and no trend with stellar mass, if taken at face value. We discuss physically-motivated alterations to the original models that bring the predictions into better agreement with the data. We argue that the measured tight size distributions of SDSS disk galaxies can be reproduced by semi-empirical models in which the $R_e-R_h$ connection is mediated by the \emph{stellar} specific angular momenta $j_{star}.$ We find that current cosmological models of galaxy formation broadly agree with our constraints for LTGs, and justify the strong link between $R_e$ and $j_{star}$ that we propose, however the tightness of the $R_e-R_h$ relation found in such ab-initio theoretical models for ETGs is in tension with our semi-empirical findings.

astro-ph.GA↗