Update documentation

* Add description on how to add Parameter sensitivites

* Add puttmann2016 and use the same format in citation.bib and
literature.bib

* Fix typo(s)

Author: jbreue16

CITATION.bib

@@ -3,65 +3,79 @@
 
 % General:
 
-@article{Leweke:2018,
-author = {Leweke, S. and von Lieres, E.},
+@article{Leweke2018CADET,
 title = {Chromatography Analysis and Design Toolkit (CADET)},
-journal = {Computers and Chemical Engineering},
-volume = {113},
 year = {2018},
-pages = {274–294},
+author = {Leweke, Samuel and von Lieres, Eric},
 doi = {10.1016/j.compchemeng.2018.02.025},
-url = {https://doi.org/10.1016/j.compchemeng.2018.02.025}
+journal = {Computers & Chemical Engineering},
+volume = {113},
+pages = {274-294},
+issn = {0098-1354},
+keywords = {Column liquid chromatography, General rate model, Modeling and simulation platform, Model calibration, Process analysis and design, Statistical analysis, Experimental design},
+abstract = {CADET is an open source modeling and simulation framework for column liquid chromatography. The software is freely distributed to both academia and industry under the GPL license (https://github.com/modsim/cadet). CADET is based on a core simulator that is written in object oriented C++ and applies modern mathematical algorithms for efficiently solving a variety of customary chromatography models. This simulation engine is interfaced to a suite of MATLAB tools for setting up and executing the most common scientific workflows, e.g., model calibration, process design, robustness analysis, statistical analysis, and experimental design. The model library and numerical methods are continuously extended and improved. For instance, binding models with multiple bound states, pH and/or temperature dependence of binding parameters, surface diffusion, and arbitrary spacing of the radial discretization have been recently added. Moreover, numerical accuracy and computational speed of the code are comprehensively benchmarked using high precision reference solutions and realistic model problems. Versatility of the CADET modeling platform is demonstrated with several examples that are also published as open source code and can be freely adapted to specific use cases. In one of several case studies, sequential and simultaneous optimization of elution gradient shape and cut times are compared for a three component separation. This process is designed to achieve Pareto optimal purity and yield of the central fraction. Moreover, the robustness of these designs with respect to typical process variations is systematically studied. The last case study illustrates the optimal design of experiments for estimating model parameters with maximal accuracy.}
 }
 
-@article{vonLieres:2010,
-author = {von Lieres, E. and Andersson, J.},
-title = {A fast and accurate solver for the general rate model of column liquid chromatography},
-journal = {Computers and Chemical Engineering},
-volume = {34},
-number = {8},
+@article{VonLieres2010a,
+title = {{A fast and accurate solver for the general rate model of column liquid chromatography}},
 year = {2010},
-pages = {1180–1191},
+author = {von Lieres, Eric and Andersson, Joel},
 doi = {10.1016/j.compchemeng.2010.03.008},
-url = {https://doi.org/10.1016/j.compchemeng.2010.03.008}
+journal = {Computers {\&} Chemical Engineering},
+issn = {00981354},
+month = aug,
+number = {8},
+pages = {1180--1191},
+volume = {34},
 }
 
 % DG discretization of transport models:
 
-@article{Breuer:2023,
-author = {Breuer, J. and Leweke, S. and Schmölder, J. and Gassner, G. and von Lieres, E.},
+@article{Breuer2023,
 title = {Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET},
-journal = {Computers and Chemical Engineering},
-volume = {177},
 year = {2023},
-pages = {108340},
+author = {Jan Michael Breuer and Samuel Leweke and Johannes Schmölder and Gregor Gassner and Eric {von Lieres}},
 doi = {10.1016/j.compchemeng.2023.108340},
-url = {https://doi.org/10.1016/j.compchemeng.2023.108340}
+journal = {Computers \& Chemical Engineering},
+volume = {177},
+pages = {108340},
+issn = {0098-1354},
 }
 
 % Crystallization:
 
-@article{Zhang1:2024,
-author = {Zhang, Wendi and Przybycien, Todd and Schmölder, Johannes and Leweke, Samuel and von Lieres, Eric},
-title = {Solving crystallization/precipitation population balance models in {CADET}, part {I}: {Nucleation} growth and growth rate dispersion in batch and continuous modes on nonuniform grids},
-journal = {Computers and Chemical Engineering},
-volume = {183},
+@article{Zhang2024,
+title = {Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids},
 year = {2024},
-pages = {108612},
+author = {Zhang, Wendi and Przybycien, Todd and Schmölder, Johannes and Leweke, Samuel and von Lieres, Eric},
 doi = {10.1016/j.compchemeng.2024.108612},
-url = {https://doi.org/10.1016/j.compchemeng.2024.108612}
+journal = {Computers \& Chemical Engineering},
+pages = {108612},
+publisher = {Elsevier},
 }
 
-% Parameter sensitivities
+% Parameter sensitivities and Algorithmic Differentiation
 
-@article{Puttmann:2013,
-title = {Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography},
-journal = {Computers & Chemical Engineering},
-volume = {56},
-pages = {46-57},
+@article{Puttmann2013,
+title = {{Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography}},
 year = {2013},
-issn = {0098-1354},
-doi = {https://doi.org/10.1016/j.compchemeng.2013.04.021},
-url = {https://www.sciencedirect.com/science/article/pii/S0098135413001440},
-author = {Andreas Püttmann and Sebastian Schnittert and Uwe Naumann and Eric {von Lieres}}
-}
+author = {Püttmann, Andreas and Schnittert, Sebastian and Naumann, Uwe and von Lieres, Eric},
+doi = {10.1016/j.compchemeng.2013.04.021},
+journal = {Computers {\&} Chemical Engineering},
+issn = {00981354},
+month = sep,
+pages = {46--57},
+volume = {56},
+}
+
+@article{Puttmann2016,
+title = {{Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities}},
+year = {2016},
+author = {Püttmann, Andreas and Schnittert, Sebastian and Leweke, Samuel and von Lieres, Eric},
+doi = {10.1016/j.ces.2015.08.050},
+journal = {Chemical Engineering Science},
+issn = {00092509},
+month = jan,
+volume = {139},
+pages = {152--162},
+}

doc/developer_guide/model_expansion.rst

@@ -93,8 +93,8 @@ Most important functionality to be implemented:
 4. System Jacobian: Owned by the unit operation. Defined given by :math:`J := \frac{\partial F}{\partial y} + \alpha \frac{\partial F}{\partial \dot{y}}`, i.e. both the state and state derivative Jacobian need to be implemented.
 5. Linear solve: Solves the system :math:`J x = b` with given :math:`b`.
 6. Algorithmic differentiation (AD): 
-   a. Parameter sensitivities: Use ``ParamType`` for all parameters and ``ResidualType`` for the residual. 
-   b. Jacobian calculation via AD (can be used to verify the analytical implementation): Use ``StateType`` for the state and ``ResidualType`` for the residual. Additionally, you need to implement the following functions to enable the AD Jacobian: ``requiredADdirs()``, ``prepareADvectors``, ``extractJacobianFromAD()``, ``useAnalyticJacobian()``. For details please refer to `Püttmann et al. <https://doi.org/10.1016/j.compchemeng.2013.04.021>`_.
+   a. Parameter sensitivities: Use ``ParamType`` for all parameters and ``ResidualType`` for the residual. A more detailed guide on parameter sensitivities can be found in the corresponding section below.
+   b. Jacobian calculation via AD (can be used to verify the analytical implementation): Use ``StateType`` for the state and ``ResidualType`` for the residual. Additionally, you need to implement the following functions to enable the AD Jacobian: ``requiredADdirs()``, ``prepareADvectors``, ``extractJacobianFromAD()``, ``useAnalyticJacobian()``. For details please refer to `Püttmann et al. (2016) <https://doi.org/10.1016/j.ces.2015.08.050>`_.
 
 Testing and Publication
 ^^^^^^^^^^^^^^^^^^^^^^^
@@ -121,3 +121,22 @@ Use ``ParamType`` and ``ResidualType`` for parameters and residual ``res`` to en
 Use ``StateType`` and ``ResidualType`` for the state ``y`` and residual ``res`` to enable the AD Jacobian. 
 
 To use AD for a new unit operation, you can either apply dense AD or, in case of a model with many states or spatial resolution, you need to think of the shape of the Jacobian and apply sparse AD. 
+
+Parameter sensitivities
+^^^^^^^^^^^^^^^^^^^^^^^
+
+Parameter sensitivity estimation in CADET-Core leverages the capabilities provided by the time integrator module `IDAS <https://sundials.readthedocs.io/en/latest/idas/index.html>`_ to compute `forward sensitivities <https://sundials.readthedocs.io/en/latest/idas/Mathematics_link.html#forward-sensitivity-analysis>`_, combined with our custom implementation for algorithmic differentiation, as described in our publication `Püttmann et al. (2016) <https://doi.org/10.1016/j.ces.2015.08.050>`_.
+To enable a parameter sensitivity for you model, you only have to take care about calling and interfacing to the existing infrastructure, which is briefly described in the following steps:
+- The parameter must be defined as an `active` type
+- In the residual function, the parameter must be used as a `ParamType`
+- The parameter must be registered, i.e. added to the `_parameters` map, e.g.
+```
+	_parameters[makeParamId(hashString("TOTAL_POROSITY"), _unitOpIdx, CompIndep, ParTypeIndep, BoundStateIndep, ReactionIndep, SectionIndep)] = &_totalPorosity;
+```
+  which creates a unique parameter ID. ALso, the dependencies of the parameter need to be specified here, e.g. if it depends on a particle type or component etc. This map is called by the modelsystem to set up the sensitivity equations.
+- If the parameter is vector valued, the sensitivities for each entry of the 1D or 2D vector can be computed.
+  To this end, you need to call the corresponding registering function, e.g.
+```
+	registerParam1DArray(_parameters, _initC, [=](bool multi, unsigned int comp) { return makeParamId(hashString("INIT_C"), _unitOpIdx, comp, ParTypeIndep, BoundStateIndep, ReactionIndep, SectionIndep); });
+```
+- CADET-Core takes care of the rest

doc/developer_guide/release_new_version.rst

@@ -1,7 +1,7 @@
 .. _release_new_version:
 
-CADET-Core version release
-==========================
+CADET-Core release
+==================
 
 CADET-Core releases follow the semantic versioning system, which is documented `here <https://semver.org/>`_.
 

doc/literature.bib

@@ -3,110 +3,110 @@
 
 @article{Leweke2018CADET,
 title = {Chromatography Analysis and Design Toolkit (CADET)},
+year = {2018},
+author = {Leweke, Samuel and von Lieres, Eric},
+doi = {10.1016/j.compchemeng.2018.02.025},
 journal = {Computers & Chemical Engineering},
 volume = {113},
 pages = {274-294},
-year = {2018},
 issn = {0098-1354},
-doi = {10.1016/j.compchemeng.2018.02.025},
-author = {Leweke, Samuel and von Lieres, Eric},
 keywords = {Column liquid chromatography, General rate model, Modeling and simulation platform, Model calibration, Process analysis and design, Statistical analysis, Experimental design},
 abstract = {CADET is an open source modeling and simulation framework for column liquid chromatography. The software is freely distributed to both academia and industry under the GPL license (https://github.com/modsim/cadet). CADET is based on a core simulator that is written in object oriented C++ and applies modern mathematical algorithms for efficiently solving a variety of customary chromatography models. This simulation engine is interfaced to a suite of MATLAB tools for setting up and executing the most common scientific workflows, e.g., model calibration, process design, robustness analysis, statistical analysis, and experimental design. The model library and numerical methods are continuously extended and improved. For instance, binding models with multiple bound states, pH and/or temperature dependence of binding parameters, surface diffusion, and arbitrary spacing of the radial discretization have been recently added. Moreover, numerical accuracy and computational speed of the code are comprehensively benchmarked using high precision reference solutions and realistic model problems. Versatility of the CADET modeling platform is demonstrated with several examples that are also published as open source code and can be freely adapted to specific use cases. In one of several case studies, sequential and simultaneous optimization of elution gradient shape and cut times are compared for a three component separation. This process is designed to achieve Pareto optimal purity and yield of the central fraction. Moreover, the robustness of these designs with respect to typical process variations is systematically studied. The last case study illustrates the optimal design of experiments for estimating model parameters with maximal accuracy.}
 }
 
 @article{VonLieres2010a,
+title = {{A fast and accurate solver for the general rate model of column liquid chromatography}},
+year = {2010},
 author = {von Lieres, Eric and Andersson, Joel},
 doi = {10.1016/j.compchemeng.2010.03.008},
-issn = {00981354},
 journal = {Computers {\&} Chemical Engineering},
+issn = {00981354},
 month = aug,
 number = {8},
 pages = {1180--1191},
-title = {{A fast and accurate solver for the general rate model of column liquid chromatography}},
 volume = {34},
-year = {2010}
 }
 
 % CADET-CORE MAJOR EXTENSIONS
 
-@article{ZHANG2025solving,
+@article{Zhang2025,
 title = {Solving crystallization/precipitation population balance models in CADET, Part II: Size-based Smoluchowski coagulation and fragmentation equations in batch and continuous modes},
+year = {2025},
+author = {Zhang, Wendi and Przybycien, Todd and Breuer, Jan Michael and von Lieres, Eric},
+doi = {10.1016/j.compchemeng.2024.108860},
 journal = {Computers & Chemical Engineering},
 volume = {192},
 pages = {108860},
-year = {2025},
 issn = {0098-1354},
-doi = {10.1016/j.compchemeng.2024.108860},
-author = {Zhang, Wendi and Przybycien, Todd and Breuer, Jan Michael and von Lieres, Eric}
 }
 
-@article{zhang2024solving,
-  title = {Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids},
-  author = {Zhang, Wendi and Przybycien, Todd and Schmölder, Johannes and Leweke, Samuel and von Lieres, Eric},
-  journal = {Computers \& Chemical Engineering},
-  pages = {108612},
-  year = {2024},
-  publisher = {Elsevier},
-  doi = {10.1016/j.compchemeng.2024.108612}
+@article{Zhang2024,
+title = {Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids},
+year = {2024},
+author = {Zhang, Wendi and Przybycien, Todd and Schmölder, Johannes and Leweke, Samuel and von Lieres, Eric},
+doi = {10.1016/j.compchemeng.2024.108612},
+journal = {Computers \& Chemical Engineering},
+pages = {108612},
+publisher = {Elsevier},
 }
 
 @article{Breuer2023,
 title = {Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET},
+year = {2023},
+author = {Jan Michael Breuer and Samuel Leweke and Johannes Schmölder and Gregor Gassner and Eric {von Lieres}},
+doi = {10.1016/j.compchemeng.2023.108340},
 journal = {Computers \& Chemical Engineering},
 volume = {177},
 pages = {108340},
-year = {2023},
 issn = {0098-1354},
-doi = {10.1016/j.compchemeng.2023.108340},
-author = {Jan Michael Breuer and Samuel Leweke and Johannes Schmölder and Gregor Gassner and Eric {von Lieres}},
 }
 
 @article{Puttmann2013,
+title = {{Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography}},
+year = {2013},
 author = {Püttmann, Andreas and Schnittert, Sebastian and Naumann, Uwe and von Lieres, Eric},
 doi = {10.1016/j.compchemeng.2013.04.021},
-issn = {00981354},
 journal = {Computers {\&} Chemical Engineering},
+issn = {00981354},
 month = sep,
 pages = {46--57},
-title = {{Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography}},
 volume = {56},
-year = {2013}
 }
 
 @article{Puttmann2016,
+title = {{Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities}},
+year = {2016},
 author = {Püttmann, Andreas and Schnittert, Sebastian and Leweke, Samuel and von Lieres, Eric},
 doi = {10.1016/j.ces.2015.08.050},
-issn = {00092509},
 journal = {Chemical Engineering Science},
+issn = {00092509},
 month = jan,
-pages = {152--162},
-title = {{Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities}},
 volume = {139},
-year = {2016}
+pages = {152--162},
 }
 
 % CADET OTHER SOFTWARE
 
 @Article{Schmoelder2020,
-  author  = {Schmölder, Johannes and Kaspereit, Malte},
   title   = {A {{Modular Framework}} for the {{Modelling}} and {{Optimization}} of {{Advanced Chromatographic Processes}}},
+  year    = {2020},
+  author  = {Schmölder, Johannes and Kaspereit, Malte},
   doi     = {10.3390/pr8010065},
+  journal = {Processes},
   number  = {1},
-  pages   = {65},
   volume  = {8},
-  journal = {Processes},
-  year    = {2020},
+  pages   = {65},
 }
 
-@article{Heymann2022advanced,
+@article{Heymann2022,
 title = {Advanced score system and automated search strategies for parameter estimation in mechanistic chromatography modeling},
+year = {2022},
+author = {William Heymann and Juliane Glaser and Fabrice Schlegel and Will Johnson and Pablo Rolandi and Eric {von Lieres}},
+doi = {https://doi.org/10.1016/j.chroma.2021.462693},
 journal = {Journal of Chromatography A},
 volume = {1661},
 pages = {462693},
-year = {2022},
 issn = {0021-9673},
-doi = {https://doi.org/10.1016/j.chroma.2021.462693},
-author = {William Heymann and Juliane Glaser and Fabrice Schlegel and Will Johnson and Pablo Rolandi and Eric {von Lieres}},
 }
 
 % CADET-CORE SELECTED USE-CASES

doc/modelling/crystallization.rst

@@ -11,7 +11,7 @@ In CADET, we chose particle size and axial coordinate as the internal and extern
 The PBM in CADET is implemented so that it can be used in any unit operation that supports reactions.
 Typical applications consider crystallization in a CSTR or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is described by the LRM without solid phase.
 
-In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to :cite:`zhang2024solving`.
+In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to :cite:`Zhang2024`.
 
 .. figure:: PBM_Part_I.png
 

doc/modelling/unit_operations/lumped_rate_model_without_pores.rst

@@ -39,7 +39,7 @@ Both quasi-stationary and dynamic binding models are supported:
 
     \begin{aligned}
         \text{quasi-stationary: }& & 0 &= f_{\text{ads}}\left( c^\ell, c^s\right), \\
-        \text{dynamic: }& & \frac{\partial q}{\partial t} &= f_{\text{ads}}\left( c^\ell, c^s\right) + f_{\text{react}}^s\left( c^\ell, c^s \right).
+        \text{dynamic: }& & \frac{\partial c^s}{\partial t} &= f_{\text{ads}}\left( c^\ell, c^s\right) + f_{\text{react}}^s\left( c^\ell, c^s \right).
     \end{aligned}
 
 By default, the following initial conditions are applied for all :math:`z \in [0,L]`:

doc/publications.rst

@@ -38,8 +38,8 @@ CADET-Core Numerics and Modeling
 .. bibliography:: literature.bib
    :filter: False
 
-   ZHANG2025solving
-   zhang2024solving
+   Zhang2025
+   Zhang2024
 
 **Publications on Parameter sensitivites and (compressed) algorithmic differentiation**