research

Publications

1. J. Hudson, MD, H. N. Najm, K. Sargsyan, Measuring Stiffness in Residual Neural Networks, submitted, 2022.

2. A. Alla, MD, C. Glusa, H. Oliveira, Control of fractional diffusion problems via dynamic programming equations, submitted, 2022, arXiv:2210.09827.

3. Y. Fan, MD, Y. Yu, H. Najm, S. Silling, Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification, accepted, 2022.

4. T. Fan, N. Trask, MD, E. Darve, Probabilistic partition of unity networks for high-dimensional regression problems, accepted, 2022, arXiv preprint arXiv:2210.02694.

5. E.A. Barros de Moraes, MD, M. Zayernouri, Nonlocal machine learning of micro-structure defect evolutions in crystalline materials, submitted, 2022, arxiv:2205.05729.

6. C. Glusa, MD, G. Capodaglio, M. Gunzburger, P. Bochev, An asymptotically compatible coupling formulation for nonlocal interface problems with jumps, accepted in SISC, 2023 arxiv:2203.07565.

7. MD et al. Machine Learning in Heterogeneous Porous Materials, submitted 2022, arxiv:2202.04137.

8. X. Xu, MD, J. Foster, C. Glusa, Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves, submitted, 2022, arxiv:2201.11146.

9. M. Pasetto, Z. Shen, MD, X. Tian,N. Trask, D. Kamensky, Efficient optimization-based quadrature for variational discretization of nonlocal problems, submitted, 2022, arxiv:2201.12391.

10. H. You, Y. Yu, MD, T. Gao, S. Silling, Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network, submitted, arXiv:2201.02217, 2021.

11. MD, M. Gulian, T. Mengesha, J. Scott, Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition, accepted in Fractional Calculus and Applied Analysis, 2022.

12. C. J. Weiss, MD, C. Glusa, Fractional Calculus for Predictive Analytics in Social Network Dynamics, SAND2021-12178 (limited release), 2021. 

13. MD, D. Littlewood, J. Trageser, M. Perego, P. Bochev, An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions, submitted, 2021, arXiv:2110.04420.

14. MD, M. Gulian, H. Olson, G. E. Karniadakis. Towards a Unified Theory of Fractional and Nonlocal Vector Calculus, Fractional Calculus and Applied Analysis, 2021, arXiv:2005.07686.

15. J. Suzuki, M. Gulian, M. Zayernouri, MD, Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials, [review paper] Jorunal of Peridynamics and Nonlocal Modeling, 2022, arxiv:2110.11531.

16. Darve, MD, R. Garrappa, A. Giusti, N. L. Rubio, On the fractional Laplacian of variable order, accepted in FCAA, 2021, arXiv:2109.01060.

17. S. Silling, MD, Y. Yu, H. You, M. Fermen-Coker, Peridynamic model for single-layer graphene obtained from coarse grained bond forces, accepted in JPER, 2021.

18. H. You, Y. Yu, S. Silling, MD, A data-driven peridynamic continuum model for upscaling molecular dynamics, accepted in CMAME, 2021, arXiv:2108.04883.

19. MD, Y. Yue, On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models, accepted in the Springer AWM series volume "Research in the Mathematics of Materials Science", 2021, arXiv:2107.04450.

20. X. Xu, C. Glusa, MD, J. Foster, A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems, accepted in CMAME, 2021, arXiv:2105.07309.

21. G. Capodaglio, MD, M. Gunzburger, P. Bochev, M. Klar, C. Vollmann, A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions, accepted in NMPDEs, 2021, arXiv:2008.11780.

22. MD, C. Glusa, A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems, accepted in NMPDEs, 2021, arXiv:2101.11765.

23. E. Aulisa, G. Capodaglio, A. Chierici, MD, Efficient quadrature rules for finite element discretizations of nonlocal equations, accepted in NMPDEs, 2021, arXiv:2101.08825.

24. X. Xu, MD, J. Foster, A machine-learning framework for peridynamic material models with physical constraints, accepted in CMAME, 2021, arXiv:2101.01095.

25. O. Burkovska, C. Glusa, MD, An optimization-based approach to parameter learning for fractional type nonlocal models, accepted in CAMWA, 2021, arXiv:2010.03666.

26. MD, M. Gunzburger, C. Vollmann, A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls, accepted in M3AS, 2021, arXiv:2005.10775.

27. MD, J.C. De los Reyes, A. Trujillo, Bilevel parameter optimization for nonlocal image denoising models, accepted in Journal of Mathematical Imaging and Vision, 2021, arXiv:1912.02347.

28. C. Glusa, MD, H. Antil, C.J. Weiss, B.G. van Bloemen Waanders A Fast Solver for the Fractional Helmholtz Equation, accepted in SISC, 2021.

29. MD, M. Gulian, Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport accepted in Numerical Mathematics: Theory, Methods and Applications, 2021, arXiv:2101.04289

30. H. You, Y. Yu, S. Silling, MD, Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws, accepted in AAAI Spring Symposium: MLPS, 2021, arXiv:2012.04157.

31. H.A. Olson, M. Gulian and M. D'Elia, The Tempered Fractional Laplacian As a Special Case of the Nonlocal Laplace Operator, in Computer Science Research Institute Summer Proceedings 2020, A.A. Rushdi and M.L. Parks, eds., Technical Report SAND2020-12580R, Sandia National Laboratories, 2020, pp. 111-126, 2020.

32. MD, P. Bochev, Formulation, Analysis and Computation of an optimization-based local-to-nonlocal coupling method, RINAM, 9, 100129, 2021.

33. G. Capodaglio, MD, P. Bochev, M. Gunzburger, An energy-based coupling approach to nonlocal interface problems, Computers and Fluids, 207, 104593, 2020.

34. MD, C. Flores, X. Li, P. Radu, Y. Yu, Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications, Journal of Peridynamics and Nonlocal Modeling, 2020, arXiv:1908.08624.

35. H. You, Y. Yu, N. Trask, M. Gulian, MD, Data-driven learning of robust nonlocal physics from high-fidelity synthetic data, CMAME, 374, 113553, 2021.

36. G. Pang, MD, M. Parks, G.E. Karniadakis. nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications, JCP, 422, 109760, 2020, arXiv:2004.04276.

37. MD, X. Tian, Y. Yu, A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints, SISC, 42(4), A1935–A1949, 2020.

38. P. Bochev, D. Ridzal, MD, M. Perego, K. Peterson, Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction, CMAME, 367, 112982, 2020.

39. MD, Q. Du, C. Glusa, M. Gunzburger, X. Tian, and Z. Zhou, Numerical methods for nonlocal and fractional models, Acta Numerica, 2020, p 1-124, arXiv:2002.01401.

40. MD, E. Phipps, A. A. Rushdi, M. S. Ebeida, Surrogate-based Ensemble Grouping Strategies for Embedded Sampling-based Uncertainty Quantification, Quantification of Uncertainty: Improving Efficiency and Technology, 41-66, D'Elia, Gunzburger, Rozza editors, 2020.

41. MD, X. Li, P. Seleson, X. Tian, Y. Yu, A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics, to appear in Journal of Peridynamics and Nonlocal Modeling, 2020, arXiv:1912.06668.

42. J.L. Suzuki, Y. Zhou, MD, M. Zayernouri, A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model with Memory-Dependent Damage for Anomalous Materials, accepted in CMAME, 373, 113494, 2020.

43. MD, C. Glusa, E. Otarola, A priori error estimates for the optimal control of the integral fractional Laplacian, SIAM Journal on Control and Optimization 57(4), 2775-2798, 2019.

44. MD, Q. Du, M. Gunzburger, R. Lehoucq, Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes, Computational Methods in Applied Mathematics, 29, 2017

45. A. A. Rushdi, L. P. Swiler, E. Phipps, MD, M. S. Ebeida, VPS: Voronoi piecewise surrogate models for high-dimensional data fitting, International Journal for Uncertainty Quantification, 7,1,1–21, 2017

46. MD, H.C. Edwards, J. Hu, E. Phipps, S. Rajamanickam, Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems, SIAM/ASA J. Uncertainty Quantification, 6(1), 87–117, 2018.

47. MD, M. Perego, P. Bochev, D. Littlewood, A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions, Computers & Mathematics with Applications, 71, 11, 2218-2230, 2016

48. MD, D. Ridzal, K.J. Peterson, P.B. Bochev, M. Shashkov, Optimization-based mesh correction with volume and convexity constraints, Journal of Computational Physics, 313, 455–477, 2016

49. E. Phipps, MD, H.C. Edwards, M. Hoemmen, J. Hu, S. Rajamanickam, Embedded Ensemble Propagation for Improving Performance, Portability and Scalability of Uncertainty Quantification on Emerging Computational Architectures, accepted for publication on SIAM Journal of Scientific Computing, 2017

50. MD, M. Gunzburger, Identification of the diffusion parameter in nonlocal steady diffusion problems, Applied Mathematics and Optimization, 73, 2, 227-249, 2016

51. MD, P. B. Bochev, Optimization-Based Coupling of Nonlocal and Local Diffusion Models, 2014 MRS Fall Meeting Proceedings, 2015

52. O. Defterli, MD, Q. Du, M. Gunzburger, R. Lehoucq, M.M. Meerschaert, Fractional diffusion on bounded domains, Fractional Calculus and Applied Analysis 18 (2), 342-360, 2015

53. N. Burch, MD, R. Lehoucq, The exit-time problem for a Markov jump process, The European Physical Journal Special Topics, 223, 3257-3271, 2014

54. MD, M. Gunzburger, Optimal distributed control of nonlocal steady diffusion problems, SIAM Journal on Control and Optimization, 52, 1, 243-273, 2014

55. MD, M. Gunzburger, The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator, Computers and Mathematics with applications, 66, 1245–1260, 2013

56. MD, M. Gunzburger, Coarse-grid sampling interpolatory methods for approximating Gaussian random fields, SIAM/ASA Journal on Uncertainty Quantification, 1, 270-296, 2013

57. MD, A. Veneziani, Uncertainty quantification for data assimilation in a steady incompressible Navier-Stokes problem, ESAIM Mathematical Modelling and Numerical Analysis, 47(04), 1037-1057, 2013

58. MD, Assimilation of velocity data into fluid dynamic simulations, an application to computational hemodynamics, Dissertation thesis, 2011

59. MD, M. Perego, A. Veneziani, A variational data assimilation procedure for the incompressible Navier-Stokes equations in hemodynamics, Journal of Scientific Computing, 52, 2, 340-359, 2012

60. MD, A. Veneziani, A data assimilation technique for including noisy measurements of the velocity field into Navier-Stokes simulations, Proceedings of V European Conference on Computational Fluid Dynamics, ECCOMAS, 2010

61. MD, A. Veneziani, Methods for assimilating blood velocity measures in hemodynamics simulations: preliminary results, Proc. Comp. Science, 2010

62. MD, L. Dedé, A. Quarteroni, Reduced Basis Method for Parametrized Differential Algebraic Equations, Bulletin of the SeMA, 46, 45-73, 2009

Book Chapters:

1. MD, Q. Du, M. Gunzburger, Recent Progress in Mathematical and Computational Aspects of Peridynamics, Chapter in Handbook of nonlocal continuum mechanics for materials and structures, Springer, 2017.

2. MD, P. Bochev, D. Littlewood, M. Perego, Optimization-based coupling of local and nonlocal models: Applications to peridynamics, Chapter in Handbook of nonlocal continuum mechanics for materials and structures, Springer, 2017

3. L. Bertagna, MD, M. Perego, A. Veneziani, Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction, Chapter in Fluid-Structure Interaction and Biomedical Applications, Springer, 2014

4. MD, L. Mirabella, T. Passerini, M. Perego, M. Piccinelli, C. Vergara and A. Veneziani, Applications of Variational Data Assimilation in Computational Hemodynamics, Chapter in Modeling of Physiological Flows, Springer, 2011

Recent and upcoming plenary lectures:

• Substructuring based domain decomposition methods for nonlocal equations, 27th Conference on Domain Decomposition methods. July 2022, Prague, CZ.

• Data driven learning of nonlocal models, bridging scales with nonlocality, Machine Learning in Heterogeneous porous materials, October 6th 2021, University of Utah, UT (Virtual).

• Nonlocal model learning: from high-fidelity simulations to nonlocal constitutive laws, ALOP Workshop on nonlocal models. July 12th, 2021, Trier, Germany (Virtual).

• A unified theory of fractional and nonlocal calculus and its consequences on nonlocal model discovery, INdAM Workshop on fractional differential equations. July 13th, 2021, Rome, Italy (Virtual).

Recent lectures and courses:

• FONM 2018, Summer School on Fractional and Other Nonlocal Models, BCAM, Bilbao, Spain, May 28-31 2018, Mathematical and numerical analysis of nonlocal models for diffusion.

• Graduate course on Nonlocal Models. MODEMAT, National Engineering School, Quito, Ecuador, October-November, 2017.

• NSFE 2017, Nonlocal School on Fractional Equations, Ames, IA, 17-19 August, 2017. A coupling strategy for local and nonlocal elasticity.

Recently organized events

• RAMSES, Reduced order models, Approximation theory, Machine Learning, Surrogates, Emulators, and Simulators, SISSA, Trieste, Italy, June 29-July2, 2020. Organizers: MD, M. Gunzburger, G. Rozza.

• Optimal Control and Optimization for nonlocal models, within the Special Semester on Optimization at RICAM, Linz, Austria. Oct 28-30, 2018. Organizers: MD, M. Gunzburger.

• MANNA, Modeling, Analysis and Numerics for Nonlocal Applications. Santa Fe, NM, USA, Dec 11-15, 2017. Organizers: MD, G.E. Karniadakis.

• QUIET, Quantification of Uncertainty: Improving Efficiency and Technology, SISSA, Trieste, Italy, July 18-22, 2017. Organizers: MD, M. Gunzburger, G. Rozza