{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T13:10:52Z","timestamp":1778764252410,"version":"3.51.4"},"reference-count":38,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171339"],"award-info":[{"award-number":["12171339"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471296"],"award-info":[{"award-number":["12471296"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1016\/j.neunet.2025.107219","type":"journal-article","created":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T11:03:28Z","timestamp":1738407808000},"page":"107219","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["FxTS-Net: Fixed-time stable learning framework for Neural ODEs"],"prefix":"10.1016","volume":"185","author":[{"given":"Chaoyang","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Zou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2716-5414","authenticated-orcid":false,"given":"Wanying","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0248-9316","authenticated-orcid":false,"given":"Nanjing","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.neunet.2025.107219_b1","doi-asserted-by":"crossref","DOI":"10.1109\/TCE.2024.3439719","article-title":"A resource-aware multi-graph neural network for urban traffic flow prediction in multi-access edge computing systems","author":"Ali","year":"2024","journal-title":"IEEE Transactions on Consumer Electronics"},{"key":"10.1016\/j.neunet.2025.107219_b2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.neunet.2021.10.021","article-title":"Exploiting dynamic spatio-temporal graph convolutional neural networks for citywide traffic flows prediction","volume":"145","author":"Ali","year":"2022","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2025.107219_b3","series-title":"Advances in neural information processing systems","article-title":"Neural ordinary differential equations","volume":"vol. 31","author":"Chen","year":"2018"},{"key":"10.1016\/j.neunet.2025.107219_b4","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2024.106549","article-title":"Adaptive decision spatio-temporal neural ODE for traffic flow forecasting with multi-kernel temporal dynamic dilation convolution","volume":"179","author":"Chu","year":"2024","journal-title":"Neural Networks"},{"issue":"2","key":"10.1016\/j.neunet.2025.107219_b5","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1049\/cvi2.12248","article-title":"Improving neural ordinary differential equations via knowledge distillation","volume":"18","author":"Chu","year":"2024","journal-title":"IET Computer Vision"},{"key":"10.1016\/j.neunet.2025.107219_b6","unstructured":"Croce, F., & Hein, M. (2020). Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. 119, In Proceedings of the 37th international conference on machine learning (pp. 2206\u20132216)."},{"key":"10.1016\/j.neunet.2025.107219_b7","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.ins.2023.03.049","article-title":"On robustness of neural ODEs image classifiers","volume":"632","author":"Cui","year":"2023","journal-title":"Information Sciences"},{"key":"10.1016\/j.neunet.2025.107219_b8","series-title":"Advances in neural information processing systems","article-title":"Efficient and accurate estimation of Lipschitz constants for deep neural networks","volume":"vol. 32","author":"Fazlyab","year":"2019"},{"key":"10.1016\/j.neunet.2025.107219_b9","series-title":"Advances in the theory of fixed-time stability with applications in constrained control and optimization","author":"Garg","year":"2021"},{"key":"10.1016\/j.neunet.2025.107219_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110314","article-title":"Fixed-time control under spatiotemporal and input constraints: A quadratic programming based approach","volume":"141","author":"Garg","year":"2022","journal-title":"Automatica"},{"key":"10.1016\/j.neunet.2025.107219_b11","unstructured":"Goodfellow, I. J., Shlens, J., & Szegedy, C. Explaining and harnessing adversarial examples, arXiv preprint arXiv:1412.6572."},{"issue":"1","key":"10.1016\/j.neunet.2025.107219_b12","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/aa9a90","article-title":"Stable architectures for deep neural networks","volume":"34","author":"Haber","year":"2017","journal-title":"Inverse Problems"},{"key":"10.1016\/j.neunet.2025.107219_b13","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image Recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 770\u2013778).","DOI":"10.1109\/CVPR.2016.90"},{"key":"10.1016\/j.neunet.2025.107219_b14","unstructured":"Hendrycks, D., & Dietterich, T. (2019). Benchmarking Neural Network Robustness to Common Corruptions and Perturbations. In International conference on learning representations."},{"key":"10.1016\/j.neunet.2025.107219_b15","series-title":"Advances in neural information processing systems","first-page":"14925","article-title":"Stable neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks","volume":"vol. 34","author":"Kang","year":"2021"},{"key":"10.1016\/j.neunet.2025.107219_b16","series-title":"Nonlinear systems; 3rd ed","author":"Khalil","year":"2002"},{"key":"10.1016\/j.neunet.2025.107219_b17","unstructured":"Kidger, P., Chen, R. T. Q., & Lyons, T. J. (2021). Hey, that\u2019s not an ODE: Faster ODE Adjoints via Seminorms. vol. 139, In Proceedings of the 38th international conference on machine learning (pp. 5443\u20135452)."},{"key":"10.1016\/j.neunet.2025.107219_b18","unstructured":"Kidger, P., Foster, J., Li, X., & Lyons, T. J. (2021). Neural SDEs as Infinite-Dimensional GANs. vol. 139, In Proceedings of the 38th international conference on machine learning (pp. 5453\u20135463)."},{"key":"10.1016\/j.neunet.2025.107219_b19","series-title":"Advances in neural information processing systems","first-page":"6696","article-title":"Neural controlled differential equations for irregular time series","volume":"vol. 33","author":"Kidger","year":"2020"},{"key":"10.1016\/j.neunet.2025.107219_b20","unstructured":"Kim, H. Torchattacks: A pytorch repository for adversarial attacks, arXiv preprint arXiv:2010.01950."},{"key":"10.1016\/j.neunet.2025.107219_b21","series-title":"Advances in neural information processing systems","article-title":"Learning stable deep dynamics models","volume":"vol. 32","author":"Kolter","year":"2019"},{"key":"10.1016\/j.neunet.2025.107219_b22","series-title":"Learning multiple layers of features from tiny images,2009","author":"Krizhevsky","year":"2007"},{"key":"10.1016\/j.neunet.2025.107219_b23","series-title":"Adversarial examples in the physical world","author":"Kurakin","year":"2018"},{"key":"10.1016\/j.neunet.2025.107219_b24","unstructured":"Latorre, F., Rolland, P., & Cevher, V. (2020). Lipschitz constant estimation of Neural Networks via sparse polynomial optimization. In International conference on learning representations."},{"key":"10.1016\/j.neunet.2025.107219_b25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2023.01.019","article-title":"Few-shot human-object interaction video recognition with transformers","volume":"163","author":"Li","year":"2023","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2025.107219_b26","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.neunet.2023.03.008","article-title":"Learning defense transformations for counterattacking adversarial examples","volume":"164","author":"Li","year":"2023","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2025.107219_b27","unstructured":"Liu, Y., Bernstein, J., Meister, M., & Yue, Y. (2021). Learning by Turning: Neural Architecture Aware Optimisation. vol. 139, In Proceedings of the 38th international conference on machine learning (pp. 6748\u20136758)."},{"key":"10.1016\/j.neunet.2025.107219_b28","unstructured":"Madry, A., Makelov, A., Schmidt, L., Tsipras, D., & Vladu, A. (2018). Towards Deep Learning Models Resistant to Adversarial Attacks. In International conference on learning representations."},{"key":"10.1016\/j.neunet.2025.107219_b29","unstructured":"Oh, Y., Lim, D., & Kim, S. (2024). Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data. In The twelfth international conference on learning representations."},{"key":"10.1016\/j.neunet.2025.107219_b30","unstructured":"Rodriguez, I. D. J., Ames, A., & Yue, Y. (2022). LyaNet: A Lyapunov Framework for Training Neural ODEs. vol. 162, In Proceedings of the 39th international conference on machine learning (pp. 18687\u201318703)."},{"issue":"3","key":"10.1016\/j.neunet.2025.107219_b31","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1007\/s10851-019-00903-1","article-title":"Deep neural networks motivated by partial differential equations","volume":"62","author":"Ruthotto","year":"2020","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"10.1016\/j.neunet.2025.107219_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2023.12.041","article-title":"Adversarially robust neural networks with feature uncertainty learning and label embedding","volume":"172","author":"Wang","year":"2024","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2025.107219_b33","unstructured":"Xiao, H. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, arXiv preprint arXiv:1708.07747."},{"key":"10.1016\/j.neunet.2025.107219_b34","unstructured":"Yan, H., Du, J., Tan, C., & Feng, J. (2020). On Robustness of Neural Ordinary Differential Equations. In International conference on learning representations."},{"key":"10.1016\/j.neunet.2025.107219_b35","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.neunet.2022.04.004","article-title":"DynamicNet: A time-variant ODE network for multi-step wind speed prediction","volume":"152","author":"Ye","year":"2022","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2025.107219_b36","series-title":"Advances in neural information processing systems","article-title":"ODE2VAE: Deep generative second order ODEs with Bayesian neural networks","volume":"vol. 32","author":"Yildiz","year":"2019"},{"key":"10.1016\/j.neunet.2025.107219_b37","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/LCSYS.2022.3186959","article-title":"Robust classification using contractive Hamiltonian neural ODEs","volume":"7","author":"Zakwan","year":"2023","journal-title":"IEEE Control Systems Letters"},{"key":"10.1016\/j.neunet.2025.107219_b38","series-title":"Advances in neural information processing systems","first-page":"3338","article-title":"Adversarial robustness in graph neural networks: A Hamiltonian approach","volume":"vol. 36","author":"Zhao","year":"2023"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360802500098X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360802500098X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T12:38:20Z","timestamp":1778762300000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S089360802500098X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5]]},"references-count":38,"alternative-id":["S089360802500098X"],"URL":"https:\/\/doi.org\/10.1016\/j.neunet.2025.107219","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[2025,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"FxTS-Net: Fixed-time stable learning framework for Neural ODEs","name":"articletitle","label":"Article Title"},{"value":"Neural Networks","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neunet.2025.107219","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"107219"}}