Research Interests

 • Applied & Computational Mathematics for Artificial Intelligence (AI)

 • Approximation Theory, Numerical/Stochastic Optimization, Scientific Computing, Applied Analysis/Probability

 • AI for Science, Scientific Machine Learning, Data-driven Discovery of Dynamics, Reduced Order Modelling, Digital Twins, and Uncertainty Quantification

Publications (google scholar)

 [24] In preparation

 [23] K. Shukl and Y.Shin, Randomized forward mode of automatic differentiation for optimization algorithms

      Submitted for publication. https://arxiv.org/abs/2310.14168

 [22] J. S. R. Park, S. W. Cheung, Y. Choi, and Y. Shin, tLaSDI: Thermodynamics-informed latent space dynamics identification

      Comput. Methods Appl. Mech. Eng., 429: 117144 (2024).

 [21] S. Lee and Y. Shin, On the training and generalization of deep operator networks

      SIAM J. Sci. Comput., 46(4), C273-C296 (2024).

 [20] J. T. Lauzon, S-W. Cheung, Y. Shin, Y. Choi, D. M. Copeland, and K. Huynh, S-OPT: A points selection algorithm for hyper-reduction in reduced order models

      SIAM J. Sci. Comput., 46(4), B474-B501 (2024).

 [19] Y. Shin, Z. Zhang, G. E. Karniadakis, Error estimates of residual minimization using neural networks for linear PDEs

      Journal of Machine Learning for Modeling and Computing, 4(4), 73-101 (2023).

 [18] Y. Shin, J. Darbon, G. E. Karniadakis, Accelerating gradient descent and Adam via fractional gradients

      Neural Networks, 161, pp. 185-201 (2023).

 [17] M. Ainsworth and Y. Shin, Active Neuron Least Squares: A training method for multivariate rectified neural networks

      SIAM J. Sci. Comput., 44(4), A2253-A2275 (2022).

 [16] B. Deng, Y. Shin, L. Lu, Z. Zhang, and G. E. Karniadakis, Approximation rates of DeepONets for learning operators arising from advection-diffusion equations,

      Neural Networks, 153, pp. 411--426 (2022).

 [15] Z. Zhang, Y. Shin, G. E. Karniadakis, GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems

       Philos. Trans. R. Soc. A. 380: 20210207 (2022).

 [14] Y. Shin, Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Networks,

       Anal. Appl. 20(1), pp. 73-119 (2022).

 [13] A. D. Jagtap, Y. Shin, K. Kawaguchi, and G. E. Karniadakis, Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

       Neurocomputing, 468, pp 165--180 (2022).

 [12] M. Ainsworth and Y. Shin, Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification, and Avoidance,

      SIAM J. Sci. Comput., 43(5), A3438-A3468 (2021).

 [11] J. Hou, Y. Shin, and D. Xiu, Identification of Corrupted Data via k-means Clustering for Function Approximation,

      CSIAM Trans. Appl. Math., 2, pp. 81-107 (2021).

 [10] Y. Shin, J. Darbon, G. E. Karniadakis, On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs,

      Commun. Comput. Phys., 28, pp. 2042-2074 (2020).

 [9] Y. Shin and G. E. Karniadakis, Trainability of ReLU Networks and Data-dependent Initialization,

       Journal of Machine Learning for Modeling and Computing, 1(1), 39-74 (2020).

 [8] L. Lu, Y. Shin, Y. Su, and G. E. Karniadakis, Dying ReLU and Initialization: Theory and Numerical Examples,

       Commun. Comput. Phys., 28, pp. 1671-1706 (2020).

 [7] Y. Shin, K. Wu and D. Xiu, Sequential function approximation using randomized samples, 

       J. Comput. Phys., 371, 363-381 (2018).

 [6] K. Wu, Y. Shin and D. Xiu, A randomized tensor quadrature method for high dimensional polynomial approximation, 

       SIAM J. Sci. Comput., 39(5), A1811-A1833 (2017).

 [5] Y. Shin and D. Xiu, A randomized algorithm for multivariate function approximation,

       SIAM J. Sci. Comput., 39(3), A983-A1002 (2017).

 [4] L. Yan, Y. Shin and D. Xiu, Sparse approximation using l1-l2 minimization and its applications to stochastic collocation, 

       SIAM J. Sci. Comput., 39(1), A229-A254 (2017).

 [3] Y. Shin and D. Xiu, Correcting data corruption errors for multivariate function approximation,

       SIAM J. Sci. Comput., 38(4), A2492-A2511 (2016).

 [2] Y. Shin and D. Xiu, On a near optimal sampling strategy for least squares polynomial regression, 

       J. Comput. Phys., 326, 931-946 (2016). 

 [1] Y. Shin and D. Xiu, Nonadaptive quasi-optimal points selection for least squares linear regression, 

       SIAM J. Sci. Comput., 38(1), A385-A411 (2016).

Conference Presentations

 [34] SIAM Computational Science and Engineering, Fort Worth, TX, Mar 2025

 [33] SIAM Mathematics of Data Science, Atlanta, GA, Oct 2024

 [32] IEEE Conference on Artificial Intelligence, Marina Bay Sands, Singapore, June 2024

 [31] North American High Order Methods Conference, Hanover, NH, June 2024. 

 [30] SIAM LA, Paris, France, May 2024.

 [29] AMS Spring Southeastern Sectional Meeting, Tallahassee, FL, Mar 2024.

 [28] SIAM UQ, Trieste, Italy, Feb-Mar 2024.

 [27] AMS Fall Southeastern Sectional Meeting, Mobile, AL, Oct 2023

 [26] ICIAM 2023, Tokyo, Japan, Aug 2023

 [25] KSIAM Spring Conference (Tutorial Lecture), Pyeongchang, Korea, May 2023

 [24] TWSIAM Annual Meeting, New Taipei, Taiwan, May 2023

 [23] KMS Spring Meeting (Invited Lecture - Applied Math), Daejeon, Korea, Apr 2023

 [22] HKUST-KAIST-NUS Joint Workshop in ACM, Hong Kong, Apr 2023

 [21] SIAM CSE 2023, Amsterdam, The Netherlands, Feb - March 2023

 [20] (Virtual) Global KMS International Conference, Seoul, Korea, Oct 2022

 [19] SIAM Mathematics of Data Science, Sept 2022

 [18] International Conference on SciML, Seoul, Korea, Aug 2022

 [17] (Virtual) SIAM UQ, Atlanta, GA, April 2022

 [16] (Virtual) SIAM Analysis of PDEs, Berlin, Germany, March 2022

 [15] (Virtual) KSIAM Annual Meeting, Busan, Korea, Dec 2021

 [14] (Virtual) The 6th Annual Meeting of SIAM Central States Section, Oct 2021

 [13] (Virtual) SIAM Southeastern Atlantic Section Conference, Auburn, AL, Sept 2021

 [12] (Virtual) SIAM CSE 2021, March 2021

 [11] (Virtual) Mathematical and Scientific Machine Learning, Princeton, July 2020

 [10] (Virtual) SIAM Mathematics of Data Science, June 2020

 [9] ICERM: Scientific Machine Learning, Jan 2019, Providence, RI, USA

 [8] SIAM UQ 2018, April 2018, Garden Grove, CA, USA

 [7] SIAM CSE 2017, Feb 2017, Atlanta, GA, USA

 [6] 12th WCCM - 6th APCOM 2016, July 2016, Seoul, Korea.

 [5] 15th International Conference Approximation Theory, May 2016, San Antonio, TX, USA.

 [4] SIAM UQ 2016, April 2016, Lausanne, Switzerland.

 [3] 14th Copper Mountain Conference on Iterative Methods, March 2016, CO, USA.

 [2] ICIAM 2015, August 2015, Beijing, China.

 [1] SIAM CSE 2015, March 2015, Salt Lake City, UT, USA

Invited talks/seminars

 [42] NCTS Optimization Workshop, Department of Mathematics, NTNU, New Taipei, Taiwan, May 2023.

 [41] KAI-X Distinguished Lecture Series, KAIST, Daejeon. Korea, May 2023. (YouTube)

 [40] Numerical Analysis Seminar, HKU, Hong Kong, Apr 2023.

 [39] Colloquium, Department of Mathematics, Yonsei University, Seoul, Korea, Apr 2023.

 [38] (Virtual) CMIT Seminar, University of Liverpool, UK, Mar 2023.

 [37] Colloquium, Department of Applied Mathematics, UC Santa Cruz, Santa Cruz, CA, USA, Feb 2023.

 [36] Colloquium, Department of Mathematics, LSU, Baton Rouge, LA, USA, Feb 2023.

 [35] Colloquium, Department of Mathematics, Virginia Tech, Blacksburg, VA, USA, Jan 2023.

 [34] Colloquium, Department of Mathematics, NCSU, Raleigh, NC, USA, Jan 2023.

 [33] Colloquium, Department of Mathematics, Emory, Atlanta, GA, USA, Jan 2023.

 [32] Colloquium, Department of Mathematics, SMU, Dallas, TX, USA, Jan 2023.

 [31] Human-Machine iNteraction Lab. Seminar, KAIST, Daejeon, Korea, Dec 2022.

 [30] MINDS Seminar Series, POSTECH, Pohang, Korea, Dec 2022.

 [29] Colloquium, Dept. of Mathematical Sciences, KAIST, Daejeon, Korea, Nov 2022.

 [28] Colloquium, Department of Mathematics, SKKU, Suwon, Korea, Nov 2022.

 [27] Colloquium, Department of Mathematical Sciences, SNU, Seoul, Korea, Oct 2022.

 [26] Center for AI and Natural Sciences, KIAS, Seoul, Korea, Oct 2022.

 [25] H&A  Research Center, LG Electronics Inc., Seoul, Korea, Sept 2022.

 [24] (Virtual) Numerical Analysis Seminar, KTH, Stockholm, Sweden, Sept 2022.

 [23] Applied Fluid Mechanics Lab. Seminar, KAIST, Daejeon, Korea, July 2022.

 [22] (Virtual) CCMA Seminar, Penn State University, State College, PA, USA, May 2022.

 [21] (Virtual) Department of Mathematics, FSU, Tallahassee, FL, USA, Jan 2022.

 [20] (Virtual) Department of Mathematics, UCLA, Los Angeles, CA, USA, Jan 2022.

 [19] Department of Mathematics, Portland State University, Portland, OR, USA, Jan 2022.

 [18] Department of Mathematics, Lehigh, Bethlehem, PA, USA, Dec 2021.

 [17] Department of Scientific Computing, FSU, Tallahassee, FL, USA, Nov 2021.

 [16] (Virtual) Comput. and Applied Math Seminar, Tufts, MA, USA, Oct 2021.

 [15] (Virtual) DDPS Seminar, LLNL, July 2021. (Youtube)

 [14] (Virtual) University of California, Riverside, CA, USA, May 2021.

 [13] (Virtual) University of Texas at El Paso, Texas, USA, Apr 2021.

 [12] (Virtual) RWTH Aachen University, Germany, Mar 2021.

 [11] (Virtual) University of Iowa, Iowa, USA, Mar 2021.

 [10] (Virtual) KAIST, Daejeon, Korea, Feb 2021.

 [9] (Virtual) Helmholtz-Zentrum Dresden-Rossendorf, Germany, Sep 2020.

 [8] (Virtual) Physics-Informed Learning Machines Webinar, PNNL, May 2020.

 [7] Department of Computational Science & Engineering Seminar, Yonsei University, Aug 2019, Seoul, Korea.

 [6] Department of Mathematical Sciences Seminar, Seoul National University, Aug 2019, Seoul, Korea.

 [5] Department of Mathematics Seminar, Yonsei University, Jan 2019, Seoul, Korea.

 [4] Applied Algebra and Optimization Research Center Seminar, Sungkyunkwan University, Jan 2019, Suwon, Korea.

 [3] Applied Mathematics Colloquium, Brown University, Sep 2018, Providence, RI, USA.

 [2] Spring School, University of South Carolina, Feb 2018, Columbia, SC, USA.

 [1] Department of Mathematics Seminar, Sungkyunkwan University, July 2016, Suwon, Korea.

Teaching

    NC State University

MA 421 Introduction to Probability

MA 587 Numerical Solution of PDEs - FEM

    KAIST

        MAS480C Introduction to Scientific Machine Learning
*This course was supported by the A.I. course Development Program from the KAIST Office of Academic Affairs

MAS557 Theory and Application of Machine Learning 

    Brown University

        APMA 1650 APMA 1655 (Honors) Statistical Inference I, [Lecture Notes]

APMA 1160 An Introduction to Numerical Optimization

        APMA 1170 Introduction to Computational Linear Algebra

        APMA 1210 Operations Research - Deterministic Models

        APMA 1360 Applied Dynamical Systems