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Numerical Approximation of a PDE‐Constrained Optimization Problem that Appears in Data‐Driven Computational Mechanics

International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.
ABSTRACT We investigate an optimization problem that arises when working within the paradigm of Data‐Driven Computational Mechanics. In the context of the diffusion‐reaction problem, such an optimization problem seeks the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The
Pedro B. Bazon, Cristian G. Gebhardt, Gustavo C. Buscaglia, Roberto F. Ausas   +3 more
wiley   +1 more source

Selection of Fitness Criteria for Learning Interpretable PDE Solutions via Symbolic Regression. [PDF]

Syst Control Trans
Cohen BG, Beykal B, Bollas GM.
europepmc   +1 more source

Novel Soliton and Periodic Wave Solutions of the (3+1)-Dimensional Shallow Water Wave Equation with Bifurcation Analysis. [PDF]

Sci Rep
Hasan WM, Ahmed HM, Ahmed AM, Rezk HM, Rabie WB.   +4 more
europepmc   +1 more source

Analytical evaluations using neural network-based method for wave solutions of combined Kairat-II-X differential equation in fluid mechanics. [PDF]

Sci Rep
Zhou P, Manafian J, Lakestani M, Ilhan OA, Bahador NJ, Fattah AA, Mahmoud KH, Nuray R, Nagiyeva N.   +8 more
europepmc   +1 more source

Sampled-data fuzzy [Formula: see text] estimators for control of nonlinear parabolic partial differential equations. [PDF]

Sci Rep
Sivakumar M, Dharani S, Cao J.
europepmc   +1 more source

Reduced order modeling with shallow recurrent decoder networks. [PDF]

Nat Commun
Tomasetto M, Williams JP, Braghin F, Manzoni A, Kutz JN.   +4 more
europepmc   +1 more source

Soliton solutions with bifurcation, sensitivity, chaotic and stability analysis of the (2+1)-dimensional Zoomeron equation using generalized Riccati equation mapping method. [PDF]

Sci Rep
Zainab A, Saad KM, Abbas M, Hamanah WM, Yousaf MZ, Birhanu A.   +5 more
europepmc   +1 more source

Temporal neural operator for modeling time-dependent physical phenomena. [PDF]

Sci Rep
Diab W, Al Kobaisi M.
europepmc   +1 more source

Parameter identification for PDEs using sparse interior data and a recurrent neural network. [PDF]

Sci Rep
Long J, Khaliq A, Furati KM.
europepmc   +1 more source

Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method. [PDF]

Sci Rep
Hussain A, Ibrahim TF, Birkea FMO, Yahya MS, Hassaballa AA, Mukalazi H.   +5 more
europepmc   +1 more source