Programs of my research group: "IPBayesML: Programs for Inverse Problems of PDEs with Bayesian and Machine Learning Methods" (https://github.com/jjx323/IPBayesML or https://gitlab.com/jjx323/ipbayesml). 

Inverse Problems + Machine Learning:

1. Basic Theory + Algorithms:

• Jun Shu, Junxiong Jia, Deyu Meng, Zongben Xu, A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws, arXiv:2604.24037, 2026. 

• Yang Zhao, Haoyu Lu, Junxiong Jia*, Tao Zhou, Functional normalizing flow for statistical inverse problems of partial differential equations, 2024, arXiv:2411.13277,  Code

• Haoyu Lu, Junxiong Jia*, Deyu Meng, Sequential Monte Carlo with Gaussian Mixture Approximation for Infinite-Dimensional Statistical Inverse Problems, 2025, Code

• Shaokang Zu, Junxiong Jia*, Zhiguo Wang, Consistency of variational inference for Besov priors in nonlinear inverse problems, Inverse Problems, 42, 055008, 2026 PDF

• Shaokang Zu, Junxiong Jia*, Deyu Meng, Consistency of variational Bayesian inference for non-linear inverse problems of partial differential equations, SIAM/ASA Journal on Uncertainty Quantification, 2026. PDF

• Junxiong Jia, Deyu Meng, Zongben Xu, Fang Yao*, Nonparametric Prior Learning in Differential Equation Modeling, Journal of the American Statistical Association, February 19, 2026, Code, PDF

• Jiaming Sui*, Junxiong Jia, Jinglai Li, Stochastic gradient descent based variational inference for infinite-dimensional inverse problems, Communications on Applied Mathematics and Computation, 29 April, 2026. 

• 贾骏雄，孟德宇，张远祥，无限维贝叶斯反演理论与算法， 中国科学：数学，55(8), 2025, 1--40. [综述论文] 

• Jiaming Sui, Junxiong Jia*, Non-centered parametric variational Bayes' approach for hierarchical inverse problems of partial differential equations, Mathematics of Computation, 93(348), 2024, 1715--1760. , Codes: https://gitlab.com/jjx323/NCP-iMFVI  or  https://github.com/jjx323/NCP-iMFVI, PDF

• Xiaohua Jing, Junxiong Jia, Xueli Song, Simultaneous uniqueness for the diffusion coefficient and initial value identification in a time-fractional diffusion equation, Applied Mathematics Letters, 156, 2024, 109149. 

• Junxiong Jia, Yanni Wu, Peijun Li, Deyu Meng, Variational inverting network for statistical inverse problems of partial differential equations, Journal of Machine Learning Research, 24(201), 1--60, 2023.  Code, PDF

• Haiqi Zhao, Jinghuai Gao, Junxiong Jia, A general method for extracting the amplitude spectrum of the seismic wavelet from the seismic traces, Inverse Problems, 39(6), 065015, 2023.

• Junxiong Jia, Peijun Li, Deyu Meng, Stein variational gradient descent on infinite-dimensional space and applications to statistical inverse problems, SIAM Journal on Numerical Analysis, 60(4), 2225-2252, 2022. PDF

• Junxiong Jia, Qian Zhao, Zongben Xu, Deyu Meng, Yee Leung, Variational Bayes' approach for functions and applications to some inverse problems, SIAM Journal on Scientific Computing, 43(1), A355-A383, 2021. PDF (arXiv)

• Junxiong Jia, Jigen Peng, Jinghuai Gao, Posterior contraction for empirical Bayesian approach to inverse problems under non-diagonal assumption,  Inverse Problems & Imaging,15(2), 201-228, 2021. PDF (arXiv)

• Changlong Wang, Junxiong Jia, Jigen Peng, Shoujin Lin, A new sparse recovery method for the inverse acoustic scattering problem, Acta Mathematicae Applicatae Sinica, English Series (A special issue for IP), 31(1), 49-66, 2020. 

• Xiaohua Jing, Junxiong Jia, Jigen Peng, Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems, Applicable Analysis, 99(15), 2609-2623, 2020. 

• Junxiong Jia, Bangyu Wu, Jigen Peng, Jinghuai Gao, Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning,  Inverse Problems, 35(7), 075003, 2019. PDF(arXiv)

• Yuanxiang Zhang, Junxiong Jia, Liang Yan, Bayesian approach to a nonlinear inverse problem for time-space fractional diffusion equation, Inverse Problems, 34 (12), 125002, 2018. （2018年度Inverse Problems编辑推荐的亮点文章）

• Angang Cui, Jigen Peng, Haiyang Li, Meng Wen, Junxiong Jia, Iterative thresholding algorithm based on non-convex method for modified l(p)-norm regularization minimization, Journal of Computational and Applied Mathematics, 347, 137--180, 2018.

• Junxiong Jia, Shigang Yue, Jigen Peng, Jinghuai Gao, Infinite-dimensional Bayesian approach for inverse scattering problems of a fractional Helmholtz equation, Journal of Functional Analysis, 275(9), 2299--2332, 2018.

• Junxiong Jia, Jigen Peng, Jinghuai Gao and Yujiao Li, Backward problem for a time-space fractional diffusion equation, Inverse Problems & Imaging, 12 (2), 773--799, 2018.  

• Junxiong Jia, Bangyu Wu, A Carleman estimate of some anisotropic space-fractional diffusion equations, Applied Mathematics Letters, 80, 1--7, 2018. 

• Junxiong Jia, Jigen Peng, Jiaqing Yang, Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem,  Journal of Differential Equations, 262 (8), 4415--4450, 2017. 

• Junxiong Jia, Jigen Peng and Jinghuai Gao, Bayesian approach to inverse problems for functions with a variable index Besov prior, Inverse Problems, 32 (8), 085006, 2016. 

2. Seismic Exploration

Journal Papers: 

• Shengrui Wang, Yisi Luo, Bangyu Wu, Jiangjun Peng, Yueming Ye, Junxiong Jia, Efficient Nonlocal Tensor Function Representation for 3-D Seismic Random Noise Attenuation, IEEE Transactions on Geoscience and Remote Sensing, 20 May 2026. 
  

• Yuting Mu, Changpeng Wang, Xin Geng, Chunxia Zhang, Jiangshe Zhang, Junxiong Jia, Seismic data reconstruction via an adaptive feature fusion network, Engineering Applications of Artificial Intelligence, 160, 2025, 111982. 

• Yide Yang, Bo Li, Bangyu Wu, and Junxiong Jia, LightUNetFault3D: A Lightweight U-Net for 3-D Seismic Fault Detection, IEEE Geoscience and Remote Sensing Letters, 22, 2025, 7506405

• Jialin Wu, Bangyu Wu, Xintao Chai, and Junxiong Jia, Physics-informed neural network seismic wavefield modeling with learnable activation function and multiscale Fourier feature mapping,  IEEE Geoscience and Remote Sensing Letters, 21, 2024, 3004905

• Qiannan Wang, Zhiguo Wang, Dengliang Gao, Zhaoqi Gao, Junxiong Jia, Jianbing Zhu, and Jinghuai Gao, Seismic attribute analysis with a combination of convolutional autoencoder and random forest in a turbidite reservoir, Geophysics, 89(1), 2024, WA207--WA217.

• Bangyu Wu, Weirong Qiu, Junxiong Jia*, Naihao Liu*, Landslide susceptibility modeling using bagging based positive-unlabeled learning, IEEE Geoscience and Remote Sensing Letters, 18(5), 766 - 770，2021

• Bangyu Wu, Wenhao Xu, Bo Li, Junxiong Jia, Trapezoid coordinate finite difference modeling of acoustic wave propagation using the CPML boundary condition, Journal of Applied Geophysics, 168, 101-106, 2019. 

• Hui Yang, Junxiong Jia, Bangyu Wu, and Jinghuai Gao, Mini-batch optimized full waveform inversion with geological constrained gradient filtering, Journal of Applied Geophysics, 152, 9--16, 2018. 

Conference Papers :

• 邱维蓉, 吴帮玉, 贾骏雄. 基于正例和未标记样本的半监督集成学习方法在滑坡易发性预测中的应用, 中国石油学会2019年物探技术研讨会论文集, 2019.

• Bangyu Wu, Bo Li, Hui Yang and Junxiong Jia, 2018, Trapezoid grid finite difference for acoustic wave modeling, SEG 2018 Workshop: Seismic Imaging, Beijing, China, 12-14 November 2018.

• Bangyu Wu, Wenhao Xu, Junxiong Jia, Bo Li, Hui Yang, Haixia Zhao and Jinghuai Gao, 2018, Convolutional perfect matched layer boundary for trapezoid grid finite difference seismic modeling, SEG Technical Program Expanded Abstracts 2018, 3989-3993.

• Junxiong Jia, Qihang Sun, Bangyu Wu, Jigen Peng, A general local adaptive regularization inversion and its iterative solution, SEG Workshop: Full-waveform Inversion and Beyond, Extended Abstract, 2017.

Forward Problems:

1. Fractional Differential Equations

• Junxiong Jia, Kexue Li, Maximum principles for a time-space fractional diffusion equation, Applied Mathematics Letters, 62, 23--28, 2016. 

• Junxiong Jia, Jigen Peng, Kexue Li, Well posedness of abstract distributed order fractional diffusion equations, Communications on Pure & Applied Analysis, 13 (2), 605--621, 2014. 

• Zhandong Mei, Jigen Peng, Junxiong Jia, A new characteristic property of Mittag-Leffler functions and fractional cosine functions, Studia Mathematica, 220 (2), 119--140, 2014. 

• Kexue Li , Jigen Peng, Junxiong Jia, Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives, Journal of Functional Analysis, 263 (2), 476--510, 2012. 

• Kexue Li, Junxiong Jia, Existence and uniqueness of mild solutions for abstract delay fractional differential equations, Computers & Mathematics with Applications, 62 (3), 1398--1404, 2011. 

2. Stochastic Differential Equations

• Kexue Li, Jigen Peng and Junxiong Jia, Explosive solutions of parabolic stochastic partial differential equations with Levy noise, Discrete and Continuous Dynamical Systems--Series A, 37(10), 5105--5125, 2017. 

3. Fluid Dynamic Equations

• Junxiong Jia, Optimal time decay of Navier-Stokes equations with low regularity initial data, Acta Mathematica Sinica, English Series, 34(5), 855--872, 2018. 

• Junxiong Jia, Jigen Peng, Kexue Li, On the decay and stability of global solutions to the 3D inhomogeneous MHD system, Communications on Pure & Applied Analysis, 16 (3), 745--780, 2017. 

• Hermano Frid, Junxiong Jia, Ronghua Pan, Global smooth solutions in R-3 to short wave-long wave interactions systems for viscous magnetohydrodynamic fluids, Journal of Differential Equations, 262 (7), 4129--4173, 2017.  

• Junxiong Jia, Jigen Peng, Jinghuai Gao, Well-posedness for compressible MHD systems with highly oscillating initial data, Journal of Mathematical Physics,  57, 081514, 2016. 

• Junxiong Jia, Jigen Peng, Optimal time decay rate for the compressible viscoelastic equations in critical spaces, Applicable Analysis, 24, 1--21, 2016. 

• Junxiong Jia, Jigen Peng, Kexue Li, On the global well-posedness of a generalized 2D Boussinesq equation, NoDEA-Nonlinear Differential Equations and Applications, 22 (4), 911--945, 2015. 

• Junxiong Jia, Ronghua Pan, On isentropic approximations in compressible euler equations, Journal of Scientific Computing, 64 (3), 745--760, 2015. 

• Junxiong Jia, Jigen Peng, Zhandong Mei, Well-posedness and time-decay for compressible viscoelastic fluids in critical Besov space, Journal of Mathematical Analysis and Applications, 418 (2), 638--675, 2014.