dolfin-adjoint 2018.1: automated adjoints for FEniCS and Firedrake
Open accessAbstract
Adjoint models play an important role in scientific computing.They enable for instance sensitivity and stability analysis, goal-oriented mesh adaptivity and optimisation.However, the derivation and implementation of adjoint models is challenging, especially for models governed by non-linear or time-dependent partial differential equations (PDEs).In (Farrell, Ham, Funke, & Rognes, 2013), the authors proposed to automatically derive adjoint models through high-level algorithmic differentiation, where the forward model is considered as a sequence of variational problems.The implementation, named dolfin-adjoint, automatically and robustly derives adjoint models for models written in the finite element software FEniCS (Logg, Mardal, Wells, & others, 2012).However, the assumption that the model consists of a sequence of variational problems can be limiting.For instance when considering Dirichlet boundary conditions that are not explicitly stated in the variational formulation, when considering complex functionals that cannot be represented as an integral, or when coupling FEniCS to other non-PDE models.
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Previous computational analyses of cell migration have identified diffusivity values from approximately 50 to 3000 μm2/hr.
“Previous computational analyses of cell migration have identified a wide range of diffusivity values, from approximately 50 to 3000μm2/hr9,40,41.”
From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [40]
The Abstract describes software for deriving adjoint models for FEniCS and Firedrake; it does not discuss cell migration or report diffusivity values. Searches for cell-migration diffusivity and the 50–3000 μm²/hr range found no passage addressing the claim. No page number is provided in our copy. (LLM, conf=0.78)
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References 4 · Cited by 208
Research works printed but not linked: 4
- Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., & Wells, G. N. (2014). Unified form language: A domain-specific language for weak formulations of partial differential equations. ACM Transactions on Mathematical Software (TOMS), 40(2), 9. doi:10.1145/2566630 · DOI
- Farrell, P. E., Ham, D. A., Funke, S. W., & Rognes, M. E. (2013). Automated derivation of the adjoint of high-level transient finite element programs. SIAM Journal on Scientific Computing, 35(4), C369-C393. doi:10.1137/120873558 · DOI
- Logg, A., Mardal, K.-A., Wells, G. N., & others. (2012). Automated solution of differential equations by the finite element method. Springer. doi:10.1007/978-3-642-23099-8 · DOI · Paper page
- Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., McRae, A. T., Bercea, G.-T., et al. (2017). Firedrake: Automating the finite element method by composing abstractions. ACM Transactions on Mathematical Software (TOMS), 43(3), 24. doi:10.1145/2998441 · DOI
- Authors
- Mitusch, S., Funke, S., & Dokken, J.
- Affiliations
- Simula Research Laboratory (NO)
- Venue
- Journal of Open Source Software
- Publisher
- The Open Journal
- Published
- 2019-06-18
- Volume
- 4
- Issue
- 38
- Pages
- 1292
- ISSN
- 2475-9066 (ISSN-L)
- OpenAlex
- W2951706529
- Cited by
- 208
- References
- 4
- Citations by year
- 2026: 24 · 2025: 32 · 2024: 45 · 2023: 31 · 2022: 45 · 2021: 21 · 2020: 10
- FWCI
- 12.97
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- The Journal of Open Source Software (publishedVersion, cc-by)
- Funders
- Imperial College London
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Methods in Computational Mathematics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Keywords
- adjoint model, automatic differentiation, FEniCS, Firedrake, finite element analysis, variational problems, sensitivity analysis, optimization, Dirichlet boundary conditions
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