arXiv subjects

Mykhaylo Zayats

Publications and source records attributed to Mykhaylo Zayats.

12 recordsLinked to original sources

arXiv2026

TokaMark: A Comprehensive Benchmark for MAST Tokamak Plasma Models

Development and operation of commercially viable fusion energy reactors such as tokamaks require accurate predictions of plasma dynamics from sparse, noisy, and incomplete sensors readings. The complexity of the underlying physics and the heterogeneity of experimental data pose formidable challenges for conventional numerical methods, and highlight the promise of modern data-native approaches. A major obstacle in realizing this potential is, however, the lack of curated, openly available datasets and standardized benchmarks. Existing fusion datasets are scarce, fragmented across institutions, facility-specific, and inconsistently annotated, which limits reproducibility and prevents a fair and scalable comparison of AI approaches. In this paper, we introduce TokaMark, a structured benchmark to evaluate AI models on real experimental data collected from the Mega Ampere Spherical Tokamak (MAST). TokaMark provides a comprehensive suite of tools designed to unify access to multi-modal fusion data and standardize evaluation protocols. The benchmark includes a curated list of 14 tasks spanning a range of physical mechanisms, exploiting a variety of diagnostics and covering multiple operational use cases. A baseline model is provided to facilitate transparent comparison and validation within a unified framework. By establishing a unified benchmark, TokaMark aims to accelerate progress in data-driven AI-based plasma modeling, contributing to the broader goal of achieving sustainable and stable fusion energy. The dataset, benchmark, documentation, and tooling are open-sourced under https://github.com/UKAEA-IBM-STFC-Fusion-FMs/tokamark_baseline.

physics.plasm-ph↗

arXiv2026

Quantum algorithms for stochastic nonlinear differential equations

Stochastic nonlinear dynamics underlie many models in engineering and computational physics, yet accurate high-dimensional simulation remains challenging. We present a quantum algorithm for a broad class of $N$-dimensional stochastic differential equations with dissipation and quadratic drift. The algorithm applies to strongly nonlinear systems with all-to-all interactions, thereby extending the scope of previously known quantum algorithms that were limited to weak nonlinearity and sparse systems. For norm-preserving drifts, a condition satisfied by key fluid dynamics discretizations, our method approximates expectation values of low-order correlation functions with rigorous error bounds at a cost polynomial in $\log{(N)}$ and linear in the evolution time. Our main technical advance is a subroutine for simulating an auxiliary system of $N$ interacting quantum harmonic oscillators with cost polylogarithmic in $N$. Finally, we formulate turbulence models, including Navier-Stokes and damped Euler equations, within this framework, opening a route to quantum simulation of strongly nonlinear SDEs governing turbulence and nonlinear wave dynamics.

quant-ph↗

arXiv2026

TokaMind: A Multi-Modal Transformer Foundation Model for Tokamak Plasma Dynamics

We present TokaMind, to our knowledge the first open-source foundation model for tokamak plasma dynamics, based on a Multi-Modal Transformer (MMT) and pretrained on heterogeneous diagnostics from the publicly available MAST dataset. TokaMind supports multiple data modalities (time-series, 2D profiles, and videos) with different sampling rates, robust missing-signal handling, and efficient task adaptation via selectively loading and freezing four model components. To represent multi-modal signals, we use a lightweight fixed-basis Discrete Cosine Transform embedding (DCT3D) and provide a clean interface for alternative embeddings (e.g., Variational Autoencoders). We evaluate TokaMind on the recently introduced MAST benchmark TokaMark, which comprises 14 tasks with heterogeneous reconstruction and forecasting objectives. Our results show that fine-tuned TokaMind outperforms the strongest benchmark baseline on all but one task. Compared with training the same architecture from scratch under a matched epoch budget, warm-start adaptation is most beneficial on demanding downstream settings, including long-horizon forecasting and high-dimensional equilibrium objectives. These findings highlight the value of multi-modal pretraining for tokamak plasma dynamics and provide a practical, extensible foundation for future fusion modeling tasks. Training code and model weights are publicly available at github.com/UKAEA-IBM-STFC-Fusion-FMs/tokamind and huggingface.co/UKAEA-IBM-STFC, respectively.

physics.plasm-ph↗

arXiv2025

Quantum simulation of a noisy classical nonlinear dynamics

We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian noise in the equation of motion and in the initial conditions. Our algorithm can approximate the expected value of any correlation function that depends on $O(1)$ variables with rigorous bounds on the approximation error. The runtime scales polynomially with $\log{N}$, $t$, $J$, and $λ_1^{-1}$, where $N$ is the total number of variables, $t$ is the evolution time, $J$ is the nonlinearity strength, and $λ_1$ is the smallest dissipation rate. However, the runtime scales exponentially with a parameter quantifying inverse relative error in the initial conditions. To the best of our knowledge, this is the first rigorous quantum algorithm capable of simulating strongly nonlinear systems with $J\gg λ_1$ at the cost poly-logarithmic in $N$ and polynomial in $t$. The considered simulation problem is shown to be BQP-complete, providing a strong evidence for a quantum advantage. We benchmark the quantum algorithm via numerical experiments by simulating a vortex flow in the 2D Navier Stokes equation.

quant-ph↗

arXiv2025

WaveGAS: Waveform Relaxation for Scaling Graph Neural Networks

With the ever-growing size of real-world graphs, numerous techniques to overcome resource limitations when training Graph Neural Networks (GNNs) have been developed. One such approach, GNNAutoScale (GAS), uses graph partitioning to enable training under constrained GPU memory. GAS also stores historical embedding vectors, which are retrieved from one-hop neighbors in other partitions, ensuring critical information is captured across partition boundaries. The historical embeddings which come from the previous training iteration are stale compared to the GAS estimated embeddings, resulting in approximation errors of the training algorithm. Furthermore, these errors accumulate over multiple layers, leading to suboptimal node embeddings. To address this shortcoming, we propose two enhancements: first, WaveGAS, inspired by waveform relaxation, performs multiple forward passes within GAS before the backward pass, refining the approximation of historical embeddings and gradients to improve accuracy; second, a gradient-tracking method that stores and utilizes more accurate historical gradients during training. Empirical results show that WaveGAS enhances GAS and achieves better accuracy, even outperforming methods that train on full graphs, thanks to its robust estimation of node embeddings.

cs.LG↗

arXiv2024

Reducing data resolution for better super-resolution: Reconstructing turbulent flows from noisy observation

A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing resolution and, then, a dynamic observer is employed to reconstruct the flow field by reversing back the lost information. We provide a theoretical analysis, which indicates a chaos synchronization of the SR observer with the reference NS flow. It is shown that, even with noisy observations, the SR observer converges toward the reference NS flow exponentially fast, and the deviation of the observer from the reference system is bounded. Counter-intuitively, our theoretical analysis shows that the deviation can be reduced by increasing the lengthscale of the spatial average, i.e., making the resolution coarser. The theoretical analysis is confirmed by numerical experiments of two-dimensional NS flows. The numerical experiments suggest that there is a critical lengthscale for the spatial average, below which making the resolution coarser improves the reconstruction.

physics.flu-dyn↗

arXiv2023

Otter-Knowledge: benchmarks of multimodal knowledge graph representation learning from different sources for drug discovery

Recent research on predicting the binding affinity between drug molecules and proteins use representations learned, through unsupervised learning techniques, from large databases of molecule SMILES and protein sequences. While these representations have significantly enhanced the predictions, they are usually based on a limited set of modalities, and they do not exploit available knowledge about existing relations among molecules and proteins. In this study, we demonstrate that by incorporating knowledge graphs from diverse sources and modalities into the sequences or SMILES representation, we can further enrich the representation and achieve state-of-the-art results for drug-target binding affinity prediction in the established Therapeutic Data Commons (TDC) benchmarks. We release a set of multimodal knowledge graphs, integrating data from seven public data sources, and containing over 30 million triples. Our intention is to foster additional research to explore how multimodal knowledge enhanced protein/molecule embeddings can improve prediction tasks, including prediction of binding affinity. We also release some pretrained models learned from our multimodal knowledge graphs, along with source code for running standard benchmark tasks for prediction of biding affinity.

cs.LG↗

arXiv2023

Information Flow in Graph Neural Networks: A Clinical Triage Use Case

Graph Neural Networks (GNNs) have gained popularity in healthcare and other domains due to their ability to process multi-modal and multi-relational graphs. However, efficient training of GNNs remains challenging, with several open research questions. In this paper, we investigate how the flow of embedding information within GNNs affects the prediction of links in Knowledge Graphs (KGs). Specifically, we propose a mathematical model that decouples the GNN connectivity from the connectivity of the graph data and evaluate the performance of GNNs in a clinical triage use case. Our results demonstrate that incorporating domain knowledge into the GNN connectivity leads to better performance than using the same connectivity as the KG or allowing unconstrained embedding propagation. Moreover, we show that negative edges play a crucial role in achieving good predictions, and that using too many GNN layers can degrade performance.

cs.LG↗

arXiv2023

A recommender for the management of chronic pain in patients undergoing spinal cord stimulation

Spinal cord stimulation (SCS) is a therapeutic approach used for the management of chronic pain. It involves the delivery of electrical impulses to the spinal cord via an implanted device, which when given suitable stimulus parameters can mask or block pain signals. Selection of optimal stimulation parameters usually happens in the clinic under the care of a provider whereas at-home SCS optimization is managed by the patient. In this paper, we propose a recommender system for the management of pain in chronic pain patients undergoing SCS. In particular, we use a contextual multi-armed bandit (CMAB) approach to develop a system that recommends SCS settings to patients with the aim of improving their condition. These recommendations, sent directly to patients though a digital health ecosystem, combined with a patient monitoring system closes the therapeutic loop around a chronic pain patient over their entire patient journey. We evaluated the system in a cohort of SCS-implanted ENVISION study subjects (Clinicaltrials.gov ID: NCT03240588) using a combination of quality of life metrics and Patient States (PS), a novel measure of holistic outcomes. SCS recommendations provided statistically significant improvement in clinical outcomes (pain and/or QoL) in 85\% of all subjects (N=21). Among subjects in moderate PS (N=7) prior to receiving recommendations, 100\% showed statistically significant improvements and 5/7 had improved PS dwell time. This analysis suggests SCS patients may benefit from SCS recommendations, resulting in additional clinical improvement on top of benefits already received from SCS therapy.

cs.AI↗

arXiv2023

Detectability and global observer design for 2D Navier-Stokes equations with uncertain inputs

We present simulation friendly detectability conditions for 2D Navier-Stokes Equation (NSE) with periodic boundary conditions, and describe a generic class of ``detectable'' observation operators: it includes pointwise evaluation of NSE's solution at interpolation nodes, and spatial average measurements. For ``detectable'' observation operators we design a global infinite-dimensional observer for NSE with uncertain possibly destabilizing inputs: in our numerical experiments we illustrate $H^1$-sensitivity of NSE to small perturbations of initial conditions, yet the observer converges for known and uncertain inputs.

math.OC↗

arXiv2022

Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks

We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to provide error correction and stabilization mechanisms. In addition, to compensate for decrease of observer's performance due to the presence of unknown destabilizing forcing, the network is designed to estimate the contribution of the unknown forcing implicitly from the data over the course of training. By running a set of numerical experiments, we demonstrate that the proposed network does recover unknown forcing from data and is capable of predicting turbulent flows in high resolution from low resolution noisy observations.

math.NA↗

arXiv2017

Localised sequential state estimation for advection dominated flows with non-Gaussian uncertainty description

This paper presents a new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of $L^\infty$-type: uncertain initial condition and model error are assumed to be pointvise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this $L^\infty$-type bounding set by a union of possibly overlapping ellipsoids, which are localized (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard $L^2$-type filter (e.g. Kalman/minimax filter) which uses Gaussian/ellipsoidal uncertainty description and observations (if any) which correspond to this sub-domain. The resulting local state estimates are stitched together by the iterative d-ADN Schwartz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples.

math.OC↗