Hard Constraints Research Articles

Learning-based Predictive LPV Control of Atmospheric Pressure Plasma Jets

Abstract Complexity of atmospheric pressure plasma jet dynamics poses a significant challenge for control design, and this letter presents a learning- and Scenario-based Model Predictive Control (ScMPC) method in the Linear Parameter-Varying (LPV) framework to tackle this challenge. By leveraging artificial neural networks, an LPV state-space representation of the system dynamics is first learned. The mismatch between this model and real plant is then estimated using Bayesian neural networks, enabling scenario generation for ScMPC design. Soft constraints are imposed in the control design formulation to ensure the feasibility of the underlying optimization problem. Results from extensive simulations are used to compare the proposed framework with a benchmark LTI-based ScMPC, demonstrating superior performance in both reference tracking and thermal dose delivery. The proposed approach allows for accurate control of plasma jets while reducing conservatism inherent in either LTI-based approaches or other robust control methods.

Three-step projected forward–backward algorithms for constrained minimization problem

Three-step projected forward–backward algorithms for constrained minimization problem

Prototype-based contrastive substructure identification for molecular property prediction.

Substructure-based representation learning has emerged as a powerful approach to featurize complex attributed graphs, with promising results in molecular property prediction (MPP). However, existing MPP methods mainly rely on manually defined rules to extract substructures. It remains an open challenge to adaptively identify meaningful substructures from numerous molecular graphs to accommodate MPP tasks. To this end, this paper proposes Prototype-based cOntrastive Substructure IdentificaTion (POSIT), a self-supervised framework to autonomously discover substructural prototypes across graphs so as to guide end-to-end molecular fragmentation. During pre-training, POSIT emphasizes two key aspects of substructure identification: firstly, it imposes a soft connectivity constraint to encourage the generation of topologically meaningful substructures; secondly, it aligns resultant substructures with derived prototypes through a prototype-substructure contrastive clustering objective, ensuring attribute-based similarity within clusters. In the fine-tuning stage, a cross-scale attention mechanism is designed to integrate substructure-level information to enhance molecular representations. The effectiveness of the POSIT framework is demonstrated by experimental results from diverse real-world datasets, covering both classification and regression tasks. Moreover, visualization analysis validates the consistency of chemical priors with identified substructures. The source code is publicly available at https://github.com/VRPharmer/POSIT.

A multi-constraint optimal puncture path planning algorithm for percutaneous interventional radiofrequency thermal fusion of the L5/S1 segments

To minimize variations in treatment outcomes of L5/S1 percutaneous intervertebral radiofrequency thermocoagulation (PIRFT) arising from physician proficiency and achieve precise quantitative risk assessment of the puncture paths. We used a self-developed deep neural network DWT-UNet for automatic segmentation of the magnetic resonance (MR) images of the L5/S1 segments into 7 key structures: L5, S1, Ilium, Disc, N5, Dura mater, and Skin, based on which a needle insertion path planning environment was modeled. Six hard constraints and 6 soft constraints were proposed based on clinical criteria for needle insertion, and the physician's experience was quantified into weights using the analytic hierarchy process and incorporated into the risk function for needle insertion paths to enhance individual case adaptability. By leveraging the proposed skin entry point sampling sub-algorithm and Kambin's triangle projection area sub-algorithm in conjunction with the analytic hierarchy process, and employing various technologies such as ray tracing, CPU multi-threading, and GPU parallel computing, a puncture path was calculated that not only met clinical hard constraints but also optimized the overall soft constraints. A surgical team conducted a subjective evaluation of the 21 needle puncture paths planned by the algorithm, and all the paths met the clinical requirements, with 95.24% of them rated excellent or good. Compared with the physician's planning results, the plans generated by the algorithm showed inferior DIlium, DS1, and Depth (P < 0.05) but much better DDura, DL5, DN5, and AKambin (P < 0.05). In the 21 cases, the planning time of the algorithm averaged 7.97±3.73 s, much shorter than that by the physicians (typically beyond 10 min). The multi-constraint optimal puncture path planning algorithm offers an efficient automated solution for PIRFT of the L5/S1 segments with great potentials for clinical application.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

T-phPINN: Physics-informed neural networks for solving 2D non-Fourier heat conduction equations

Non-Fourier heat conduction plays a dominant role in many extreme transient heat conduction processes, such as laser pulses and heat transfer in biological systems, but the heat wave effect makes it difficult to solve the temperature field accurately and quickly. In order to solve this problem, the first order time derivative enhanced parallel hard constraints physics-informed neural networks (T-phPINN) is proposed. T-phPINN comprises two subnetworks and incorporates a first order time derivative to capture sharp temperature changes. Two numerical cases show that the minimum relative error of T-phPINN is 0.001 % and 0.015 %, which is 1.04 % and 12.30 % of the error of conventional PINN respectively, proving the accuracy of our architecture. A transfer learning framework is established for scenarios of different parameters, the training only requires 1/6 iterations of the basic model, and close accuracy is obtained. The computational cost of T-phPINN is evaluated using the finite element method as the baseline. For the two cases, the single calculation time is 33.43 % and 51.50 % of the baseline, while the multiple calculation time under the acceleration of transfer learning is 11.59 % and 17.75 % of the baseline. This study will be helpful for solving large-scale non-Fourier heat conduction equations precisely and expeditiously.

HyPhAICC v1.0: a hybrid physics–AI approach for probability fields advection shown through an application to cloud cover nowcasting

Abstract. This work proposes a hybrid approach that combines physics and artificial intelligence (AI) for cloud cover nowcasting. It addresses the limitations of traditional deep-learning methods in producing realistic and physically consistent results that can generalise to unseen data. The proposed approach, named HyPhAICC, enforces a physical behaviour. In the first model, denoted as HyPhAICC-1, a multi-level advection dynamics is considered a hard constraint for a trained U-Net model. Our experiments show that the hybrid formulation outperforms not only traditional deep-learning methods but also the EUMETSAT Extrapolated Imagery model (EXIM) in terms of both qualitative and quantitative results. In particular, we illustrate that the hybrid model preserves more details and achieves higher scores based on similarity metrics in comparison to U-Net. Remarkably, these improvements are achieved while using only one-third of the data required by the other models. Another model, denoted as HyPhAICC-2, adds a source term to the advection equation, it impaired the visual rendering but displayed the best performance in terms of accuracy. These results suggest that the proposed hybrid physics–AI architecture provides a promising solution to overcome the limitations of classical AI methods and contributes to open up new possibilities for combining physical knowledge with deep-learning models.

Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization Algorithm

One of the most prominent application areas for quantum computers is solving hard constraint satisfaction and optimization problems. However, detailed analyses of the complexity of standard quantum algorithms have suggested that outperforming classical methods for these problems would require extremely large and powerful quantum computers. The quantum approximate optimization algorithm (QAOA) is designed for near-term quantum computers, yet previous work has shown strong limitations on the ability of QAOA to outperform classical algorithms for optimization problems. Here we instead apply QAOA to hard constraint satisfaction problems, where both classical and quantum algorithms are expected to require exponential time. We analytically characterize the average success probability of QAOA on a constraint satisfaction problem commonly studied using statistical physics methods: random k-SAT at the threshold for satisfiability, as the number of variables n goes to infinity. We complement these theoretical results with numerical experiments on the performance of QAOA for small n, which match the limiting theoretical bounds closely. We then compare QAOA with leading classical solvers. For random 8-SAT, we find that for more than 14 quantum circuit layers, QAOA achieves more efficient scaling than the highest-performance classical solver we tested, WalkSATlm. Our results suggest that near-term quantum algorithms for solving constraint satisfaction problems may outperform their classical counterparts. Published by the American Physical Society 2024

Inferring cancer type-specific patterns of metastatic spread.

The metastatic spread of a cancer can be reconstructed from DNA sequencing of primary and metastatic tumours, but doing so requires solving a challenging combinatorial optimization problem. This problem often has multiple solutions that cannot be distinguished based on current maximum parsimony principles alone. Current algorithms use ad hoc criteria to select among these solutions, and decide, a priori, what patterns of metastatic spread are more likely, which is itself a key question posed by studies of metastasis seeking to use these tools. Here we introduce Metient, a freely available open-source tool which proposes multiple possible hypotheses of metastatic spread in a cohort of patients and rescores these hypotheses using independent data on genetic distance of metastasizing clones and organotropism. Metient is more accurate and is up to 50x faster than current state-of-the-art. Given a cohort of patients, Metient can calibrate its parsimony criteria, thereby identifying shared patterns of metastatic dissemination in the cohort. Reanalyzing metastasis in 169 patients based on 490 tumors, Metient automatically identifies cancer type-specific trends of metastatic dissemination in melanoma, high-risk neuroblastoma and non-small cell lung cancer. Metient's reconstructions usually agree with semi-manual expert analysis, however, in many patients, Metient identifies more plausible migration histories than experts, and further finds that polyclonal seeding of metastases is more common than previously reported. By removing the need for hard constraints on what patterns of metastatic spread are most likely, Metient introduces a way to further our understanding of cancer type-specific metastatic spread.

Vehicle routing problem for omnichannel retailing including multiple types of time windows and products

This paper addresses the capacitated vehicle routing problem for omnichannel retailing with multiple types of time windows (hard time windows and soft time windows) and multiple types of products simultaneously. The problem aims to transfer multiple products from a central warehouse to stores and satellites, where split delivery is allowed since the demands of stores or satellites are large and the different product types have different volumes. Based on different characteristics of purchasing channels, the time window of a store is a hard constraint while the time window of a satellite is a soft one. This type of vehicle routing problem exists extensively in omnichannel retail distribution systems in the logistics industry of China, which considers multiple purchasing channels for customers. Since this type of vehicle routing problem is an NP-hard problem and more complicated than the conventional vehicle routing problem with time windows, we design an adaptive large neighborhood search (ALNS) method to solve it. Finally, numerical experiments are conducted to evaluate the effectiveness of the proposed algorithm and reveal some managerial insights. The numerical experiments show that the proposed algorithm can obtain a high-quality solution under a shorter computation time compared with the state-of-the-art MIP solver (Gurobi).

Joint spatial constrained energy minimization for gas identification in hyperspectral imaging

Hyperspectral gas identification plays a crucial role in a variety of applications ranging from environmental monitoring to national security. Constrained Energy Minimization (CEM) constitutes a pivotal approach in hyperspectral gas target identification, emphasizing the enhancement of target signal output energy and the suppression of background signal output energy through the design of specialized filters. However, conventional CEM algorithms present notable deficiencies, notably their failure to fully exploit spatial information in hyperspectral image target recognition and their ineffectiveness in detecting targets over extensive areas. To address these challenges, a hyperspectral gas identification method named Joint Spatial Constrained Energy Minimization (JSCEM) was introduced. This method incorporates adaptive weight constraints and employs “pseudo background spectrum” techniques, integrating spatial data to improve target discernment and refining the estimation accuracy of the background autocorrelation matrix. Experimental validations involving both simulated and manual data have shown that the JSCEM method offers marked improvements in the detection of large-area gas targets within hyperspectral image. Simulation data indicate that the detection performance of the JSCEM method is significantly enhanced compared to various existing CEM algorithms. Furthermore, measured data confirm that the JSCEM algorithm accurately identifies large gas targets in hyperspectral images, offering a precise approach to gas detection. This advancement is expected to be valuable in industries requiring accurate and efficient gas identification.

Generative Variational-Contrastive Learning for Self-Supervised Point Cloud Representation.

Self-supervised representation learning for 3D point clouds has attracted increasing attention. However, existing methods in the field of 3D computer vision generally use fixed embeddings to represent the latent features, and impose hard constraints on the embeddings to make the latent feature values of the positive samples converge to consistency, which limits the ability of feature extractors to generalize over different data domains. To address this issue, we propose a Generative Variational-Contrastive Learning (GVC) model, where Gaussian distribution is used to construct a continuous, smoothed representation of the latent features. A distribution constraint and cross-supervision are constructed to improve the transfer ability of the feature extractor over synthetic and real-world data. Specifically, we design a variational contrastive module to constrain the feature distribution instead of feature values corresponding to each sample in the latent space. Moreover, a generative cross-supervision module is introduced to preserve the invariance features and promote the consistency of feature distribution among positive samples. Experimental results demonstrate that GVC achieves SOTA on different downstream tasks. In particular, with only pre-training on the synthetic dataset, GVC achieves a lead of 8.4% and 14.2% when transferring to the real-world dataset in the linear classification and few-shot classification.

PSD-ELGAN: A pseudo self-distillation based CycleGAN with enhanced local adversarial interaction for single image dehazing

Compared to pixel-level content loss, domain-level style loss in CycleGAN-based dehazing algorithms just imposes relatively soft constraints on the intermediate translated images, resulting in struggling to accurately model haze-free features from real hazy scenes. Furthermore, globally perceptual discriminator may misclassify real hazy images with significant scene depth variations as clean style, thereby resulting in severe haze residue. To address these issues, we propose a pseudo self-distillation based CycleGAN with enhanced local adversarial interaction for image dehazing, termed as PSD-ELGAN. On the one hand, we leverage the characteristic of CycleGAN to generate pseudo image pairs during training. Knowledge distillation is employed in this unsupervised framework to transfer the informative high-quality features from the self-reconstruction network of real clean images to the dehazing generator of paired pseudo hazy images, which effectively improves its haze-free feature representation ability without increasing network parameters. On the other hand, in the output of dehazing generator, four non-uniform image patches severely affected by residual haze are adaptively selected as input samples. The local discriminator could easily distinguish their hazy style, thereby further compelling the dehazing generator to suppress haze residues in such regions, thus enhancing its dehazing performance. Extensive experiments show that our PSD-ELGAN can achieve promising results and better generality across various datasets.

A train trajectory optimization method based on the safety reinforcement learning with a relaxed dynamic reward

Train trajectory optimization (TTO) is an effective way to address energy consumption in rail transit. Reinforcement learning (RL), an excellent optimization method, has been used to solve TTO problems. Although traditional RL algorithms use penalty functions to restrict the random exploration behavior of agents, they cannot fully guarantee the safety of the process and results. This paper proposes a proximal policy optimization based safety reinforcement learning framework (S-PPO) for the train trajectory optimization, including a safe action rechoosing mechanism (SARM) and a relaxed dynamic reward mechanism (RDRM) combining a relaxed sparse reward and a dynamic dense reward. SARM guarantees that the new states generated by the agent consistently adhere to the environmental security constraints, thereby enhancing sampling efficiency and facilitating algorithm convergence. RDRM makes it easier for agents to obtain successful samples by relaxing time constraints, which also offers a better balance between exploration and exploitation. The experimental results show that S-PPO can significantly improve performance and obtain better train operation trajectories than soft constraint methods, and the convergence process is smoother. Finally, it was demonstrated that S-PPO exhibits good adaptability across various speed limit tracks.

Myo-regressor Deep Informed Neural NetwOrk (Myo-DINO) for fast MR parameters mapping in neuromuscular disorders

Magnetic Resonance (MR) parameters mapping in muscle Magnetic Resonance Imaging (mMRI) is predominantly performed using pattern recognition-based algorithms, which are characterised by high computational costs and scalability issues in the context of multi-parametric mapping.Deep Learning (DL) has been demonstrated to be a robust and efficient method for rapid MR parameters mapping. However, its application in mMRI domain to investigate Neuromuscular Disorders (NMDs) has not yet been explored. In addition, data-driven DL models suffered in interpretation and explainability of the learning process. We developed a Physics Informed Neural Network called Myo-Regressor Deep Informed Neural NetwOrk (Myo-DINO) for efficient and explainable Fat Fraction (FF), water-T2 (wT2) and B1 mapping from a cohort of NMDs.A total of 2165 slices (232 subjects) from Multi-Echo Spin Echo (MESE) images were selected as the input dataset for which FF, wT2,B1 ground truth maps were computed using the MyoQMRI toolbox. This toolbox exploits the Extended Phase Graph (EPG) theory with a two-component model (water and fat signal) and slice profile to simulate the signal evolution in the MESE framework. A customized U-Net architecture was implemented as the Myo-DINO architecture. The squared L2 norm loss was complemented by two distinct physics models to define two ‘Physics-Informed’ loss functions: Cycling Loss 1 embedded a mono-exponential model to describe the relaxation of water protons, while Cycling Loss 2 incorporated the EPG theory with slice profile to model the magnetization dephasing under the effect of gradients and RF pulses. The Myo-DINO was trained with the hyperparameter value of the 'Physics-Informed' component held constant, i.e. λmodel = 1, while different hyperparameter values (λcnn) were applied to the squared L2 norm component in both the cycling loss. In particular, hard (λcnn=10), normal (λcnn=1) and self-supervised (λcnn=0) constraints were applied to gradually decrease the impact of the squared L2 norm component on the ‘Physics Informed’ term during the Myo-DINO training process.Myo-DINO achieved higher performance with Cycling Loss 2 for FF, wT2 and B1 prediction. In particular, high reconstruction similarity and quality (Structural Similarity Index > 0.92, Peak Signal to Noise ratio > 30.0 db) and small reconstruction error (Normalized Root Mean Squared Error < 0.038) to the reference maps were shown with self-supervised weighting of the Cycling Loss 2. In addition muscle-wise FF, wT2 and B1 predicted values showed good agreement with the reference values. The Myo-DINO has been demonstrated to be a robust and efficient workflow for MR parameters mapping in the context of mMRI. This provides preliminary evidence that it can be an effective alternative to the reference post-processing algorithm. In addition, our results demonstrate that Cycling Loss 2, which incorporates the Extended Phase Graph (EPG) model, provides the most robust and relevant physical constraints for Myo-DINO in this multi-parameter regression task. The use of Cycling Loss 2 with self-supervised constraint improved the explainability of the learning process because the network acquired domain knowledge solely in accordance with the assumptions of the EPG model.

Dynamic Framing and Power Allocation for Real-Time Wireless Networks with Variable-Length Coding: A Tandem Queue Approach

Ensuring high reliability and low latency poses challenges for numerous applications that require rigid performance guarantees, such as industrial automation and autonomous vehicles. Our research primarily concentrates on addressing the real-time requirements of ultra-reliable low-latency communication (URLLC). Specifically, we tackle the challenge of hard delay constraints in real-time transmission systems, overcoming this obstacle through a finite blocklength coding scheme. In the physical layer, we encode randomly arriving packets using a variable-length coding scheme and transmit the encoded symbols by truncated channel inversion over parallel channels. In the network layer, we model the encoding and transmission processes as tandem queues. These queues backlog the data bits waiting to be encoded and the encoded symbols to be transmitted, respectively. This way, we represent the system as a two-dimensional Markov chain. By focusing on instances when the symbol queue is empty, we simplify the Markov chain into a one-dimensional Markov chain, with the packet queue being the system state. This approach allows us to analytically express power consumption and formulate a power minimization problem under hard delay constraints. Finally, we propose a heuristic algorithm to solve the problem and provide an extensive evaluation of the trade-offs between the hard delay constraint and power consumption.

Piston aero-engine fault cross-domain diagnosis based on unpaired generative transfer learning

As artificial intelligence (AI) and machine learning continue to advance, they have become key players in signal analysis and pattern recognition. However, challenges such as domain shift and a lack of labeled data hinder the application of machine learning to new, unfamiliar signals, particularly in the development of intelligent diagnostic methods for mechanical faults. In this study, we address these challenges by framing them as the extreme class imbalance problem. We introduce a novel generative transfer learning framework that leverages cycle-consistent adversarial networks with hard constraints (CycleGAN-HCs). This framework is designed to generate unpaired mechanical fault signals, which are then used to train classifiers that can operate across different domains. To enhance feature extraction capabilities for time series data, we developed a new generator model called U-Attention. Additionally, we refined the training loss function to better capture domain-specific and classification-specific features in mechanical vibration signals. The proposed method successfully facilitates feature transfer and data augmentation. Its effectiveness and reliability have been demonstrated through four cross-domain fault diagnosis tasks involving piston aero-engines. Comparative verification shows that the generative transfer learning diagnostic framework outperforms traditional methods, offering superior performance and better generalization in complex mechanical fault diagnosis scenarios.

UNIFY: A unified policy designing framework for solving integrated Constrained Optimization and Machine Learning problems

The integration of Machine Learning (ML) and Constrained Optimization (CO) techniques has recently gained significant interest. While pure CO methods struggle with scalability and robustness, and ML methods like constrained Reinforcement Learning (RL) face difficulties with combinatorial decision spaces and hard constraints, a hybrid approach shows promise. However, multi-stage decision-making under uncertainty remains challenging for current methods, which often rely on restrictive assumptions or specialized algorithms. This paper introduces unify, a versatile framework for tackling a wide range of problems, including multi-stage decision-making under uncertainty, using standard ML and CO components. unify integrates a CO problem with an unconstrained ML model through parameters controlled by the ML model, guiding the decision process. This ensures feasible decisions, minimal costs over time, and robustness to uncertainty. In the empirical evaluation, unify demonstrates its capability to address problems typically handled by Decision Focused Learning, Constrained RL, and Stochastic Optimization. While not always outperforming specialized methods, unify’s flexibility offers broader applicability and maintainability. The paper includes the method’s formalization and empirical evaluation through case studies in energy management and production scheduling, concluding with future research directions.

Nonlinear stability of smooth multi-solitons for the Dullin-Gottwald-Holm equation

In this work, the stability of exact smooth multi-solitons for the Dullin-Gottwald-Holm (DGH) equation is investigated for the first time. Firstly, through the inverse scattering approach, we derive the conservation laws in terms of scattering data and multi-solitons related to the discrete spectrum based on the Lax pair of the DGH equation. Notably, a new series Hamiltonian derived from bi-Hamilton structure are equivalent to the conservation laws, and can also be expressed in terms of scattering data. Thus we successfully connect scattering data (multi-solitons) to the recursion operator between Hamiltonian, and to the Lyapunov functional constructed from Hamiltonian. With this Lyapunov functional, it is identified that these smooth multi-solitons serve as non-isolated constrained minimizers, adhering to a suitable variational nonlocal elliptic equation. Moreover, the integrable properties of the recursion operator are presented, which is the crucial for spectral analysis in this work. Consequently, the investigation of dynamical stability transforms into a problem on the spectrum of explicit linearized systems. It is worth noting that, compared to previous works on Camassa-Holm equation and KdV-type equations, recursion operator derived from existing Hamiltonian for the DGH equation do not possess good integrable properties. We construct a new series of Hamiltonians with both analysable recursion operator and simple initial variation derivative (δH1/δu=m) to overcome this problem. Furthermore, orbital stability of the smooth double solitons is proved at last of the work.

Resource potential evaluation of magmatic cobalt and nickel in the east Kunlun metallogenic belt, northwest of China through a geological-constrained convolutional neural network model

In the Kunlun orogenic belt of the East Kunlun region, several magmatic sulfide deposits of cobalt–nickel type, such as Xiarihamu and Shitoukengde, have been discovered along the Kunlun fault. The area still holds significant mineral exploration potential. This paper proposes a convolutional neural network (CNN) model based on geological constraints. When constructing the CNN model, a layer is added to restrict the magnesium-iron ratio content of mafic–ultramafic rocks in the convolutional layer, based on the characteristics of mafic–ultramafic rocks in cobalt–nickel deposits. This layer acts as a hard constraint to filter mafic–ultramafic rocks in the evidence layer, providing theoretical interpretability to the data-driven CNN model. To ensure sample balance in the prediction data and prevent overfitting during the model prediction process, a sliding window method is adopted to expand the positive samples. Predictive models are established before and after sample expansion, and ROC is used to evaluate the predictive models. Based on research into the metallogenic geological background and metallogenic model of the East Kunlun Orogenic Belt, combined with multi-source geological, geophysical, and geochemical data, a geological-constrained CNN model was used to analyze the mineralization potential of magmatic cobalt–nickel deposits in the study area. The research results show that the accuracy of the geology-constrained CNN model is 92.1 %, indicating excellent predictive performance. The results, highly consistent with known deposits, suggest that the model’s predictions can be used for resource potential assessment of magmatic cobalt–nickel deposits in the East Kunlun metallogenic belt in northwest China.