3.1 Algorithmic Differentiation

Participants: Laurent Hascoët, Jean-Luc Bouchot.

Algorithmic Differentiation (AD) differentiates programs. The input of AD is a source program $P$ that, given some $X\in {ℝ}^n$, returns some $Y=F\left(X\right)\in {ℝ}^m$, for a differentiable $F$. AD generates a new source program $P^{\text{'}}$ that, given $X$, computes some derivatives of $F$ 4.

Any execution of $P$ amounts to a sequence of instructions, which is identified with a composition of vector functions. Thus, if

where each $f_k$ is the elementary function implemented by instruction $I_k$. AD applies the chain rule to obtain derivatives of $F$. Calling $X_k$ the values of all variables after instruction $I_k$, i.e. $X_0=X$ and $X_k=f_k\left(X_{k-1}\right)$, the Jacobian of $F$ is

which can be mechanically written as a sequence of instructions $I_k^{\text{'}}$. This can be generalized to higher level derivatives, Taylor series, etc. Combining the $I_k^{\text{'}}$ with the control of $P$ yields $P^{\text{'}}$, and therefore this differentiation is piecewise.

The above computation of $F^{\text{'}}\left(X\right)$, albeit simple and mechanical, can be prohibitively expensive on large codes. In practice, many applications only need cheaper projections of $F^{\text{'}}\left(X\right)$ such as:

• Sensitivities, defined for a given direction $\dot{X}$ in the input space as:

  $$F^{\text{'}}\left(X\right).\dot{X}=f_p^{\text{'}}\left(X_{p-1}\right).f_{p-1}^{\text{'}}\left(X_{p-2}\right).\cdots .f_1^{\text{'}}\left(X_0\right).\dot{X}.$$ 2

  This expression is easily computed from right to left, interleaved with the original program instructions. This is the tangent mode of AD.

• Adjoints, defined after transposition ($F^{\text{'}*}$), for a given weighting $\overline{Y}$ of the outputs as:

  $$F^{\text{'}*}\left(X\right).\overline{Y}=f_1^{\text{'}*}\left(X_0\right).f_2^{\text{'}*}\left(X_1\right).\cdots .f_{p-1}^{\text{'}*}\left(X_{p-2}\right).f_p^{\text{'}*}\left(X_{p-1}\right).\overline{Y}.$$ 3

  This expression is most efficiently computed from right to left, because matrix$\times$vector products are cheaper than matrix$\times$matrix products. This is the adjoint mode of AD, most effective for optimization, data assimilation  32, adjoint problems  24, or inverse problems.

Adjoint AD builds a very efficient program  26, which computes the gradient in a time independent from the number of parameters $n$. In contrast, computing the same gradient with the tangent mode would require running the tangent differentiated program $n$ times.

However, the $X_k$ are required in the inverse of their computation order. If the original program overwrites a part of $X_k$, the differentiated program must restore $X_k$ before it is used by $f_{k+1}^{\text{'}*}\left(X_k\right)$. Therefore, the central research problem of adjoint AD is to make the $X_k$ available in reverse order at the cheapest cost, using strategies that combine storage, repeated forward computation from available previous values, or even inverted computation from available later values.

Another research issue is to make the AD model cope with the constant evolution of modern language constructs. From the old days of Fortran77, novelties include pointers and dynamic allocation, modularity, structured data types, objects, vectorial notation and parallel programming. We keep developing our models and tools to handle these new constructs.

3.2 Static Analysis and Transformation of programs

Participants: Laurent Hascoët, Jean-Luc Bouchot.

The most obvious example of a program transformation tool is certainly a compiler. Other examples are program translators, that go from one language or formalism to another, or optimizers, that transform a program to make it run better. AD is just one such transformation. These tools share the technological basis that lets them implement the sophisticated analyses  15 required. In particular there are common mathematical models to specify these analyses and analyze their properties.

An important principle is abstraction: the core of a compiler should not bother about syntactic details of the compiled program. The optimization and code generation phases must be independent from the particular input programming language. This is generally achieved using language-specific front-ends, language-independent middle-ends, and target-specific back-ends. In the middle-end, analysis can concentrate on the semantics of a reduced set of constructs. This analysis operates on an abstract representation of programs made of one call graph, whose nodes are themselves flow graphs whose nodes (basic blocks) contain abstract syntax trees for the individual atomic instructions. To each level are attached symbol tables, nested to capture scoping.

Static program analysis can be defined on this internal representation, which is largely language independent. The simplest analyses on trees can be specified with inference rules  18, 27, 16. But many data-flow analyses are more complex, and better defined on graphs than on trees. Since both call graphs and flow graphs may be cyclic, these global analyses will be solved iteratively. Abstract Interpretation  19 is a theoretical framework to study complexity and termination of these analyses.

Data flow analyses must be carefully designed to avoid or control combinatorial explosion. At the call graph level, they can run bottom-up or top-down, and they yield more accurate results when they take into account the different call sites of each procedure, which is called context sensitivity. At the flow graph level, they can run forwards or backwards, and yield more accurate results when they take into account only the possible execution flows resulting from possible control, which is called flow sensitivity.

Even then, data flow analyses are limited, because they are static and thus have very little knowledge of actual run-time values. Far before reaching the very theoretical limit of undecidability, one reaches practical limitations to how much information one can infer from programs that use arrays  35, 20 or pointers. Therefore, conservative over-approximations must be made, leading to derivative code less efficient than ideal.

3.3 Algorithmic Differentiation and Scientific Computing

Participants: Alain Dervieux, Laurent Hascoët, Bruno Koobus, Stephen Wornom, Jean-Luc Bouchot.

Scientific Computing provides reliable simulations of complex systems. For example it is possible to simulate the steady or unsteady 3D air flow around a plane that captures the physical phenomena of shocks and turbulence. Next comes optimization, one degree higher in complexity because it repeatedly simulates and applies gradient-based optimization steps until an optimum is reached. The next sophistication is robustness, that detects undesirable solutions which, although maybe optimal, are very sensitive to uncertainty on design parameters or on manufacturing tolerances. This makes second derivatives come into play. Similarly Uncertainty Quantification can use second derivatives to evaluate how uncertainty on the simulation inputs imply uncertainty on its outputs.

To obtain this gradient and possibly higher derivatives, we advocate adjoint AD (cf.  3.1) of the program that discretizes and solves the direct system. This gives the exact gradient of the discrete function computed by the program, which is quicker and more sound than differentiating the original mathematical equations  24. Theoretical results  23 guarantee convergence of these derivatives when the direct program converges. This approach is highly mechanizable. However, it requires careful study and special developments of the AD model  28, 33 to master possibly heavy memory usage. Among these additional developments, we promote in particular specialized AD models for Fixed-Point iterations  25, 17, efficient adjoints for linear algebra operators such as solvers, or exploitation of parallel properties of the adjoint code.

4.1 Algorithmic Differentiation

Algorithmic Differentiation of programs gives sensitivities or gradients, useful for instance for :

• optimum shape design under constraints, multidisciplinary optimization, and more generally any algorithm based on local linearization,
• inverse problems, such as parameter estimation and in particular 4Dvar data assimilation in climate sciences (meteorology, oceanography),
• first-order linearization of complex systems, or higher-order simulations, yielding reduced models for simulation of complex systems around a given state,
• adaptation of parameters for classification tools such as Machine Learning systems, in which Adjoint Differentiation is also known as backpropagation.
• mesh adaptation and mesh optimization with gradients or adjoints,
• equation solving with the Newton method,
• sensitivity analysis, propagation of truncation errors.

4.2 Multidisciplinary optimization

A CFD program computes the flow around a shape, starting from a number of inputs that define the shape and other parameters. On this flow one can define optimization criteria e.g. the lift of an aircraft. To optimize a criterion by a gradient descent, one needs the gradient of the criterion with respect to all inputs, and possibly additional gradients when there are constraints. Adjoint AD is the most efficient way to compute these gradients.

4.3 Inverse problems and Data Assimilation

Inverse problems aim at estimating the value of hidden parameters from other measurable values, that depend on the hidden parameters through a system of equations. For example, the hidden parameter might be the shape of the ocean floor, and the measurable values of the altitude and velocities of the surface. Figure 1 shows an example of an inverse problem using the glaciology code ALIF (a pure C version of ISSM  31) and its AD-adjoint produced by Tapenade.

Show image description

Six plots of fields of physical values on Pine Island Glacier, West Antarctica, showing resolution of an inverse problem

One particular case of inverse problems is data assimilation  32 in weather forecasting or in oceanography. The quality of the initial state of the simulation conditions the quality of the prediction. But this initial state is not well known. Only some measurements at arbitrary places and times are available. A good initial state is found by solving a least squares problem between the measurements and a guessed initial state which itself must verify the equations of meteorology. This boils down to solving an adjoint problem, which can be done though AD  34. The special case of 4Dvar data assimilation is particularly challenging. The 4th dimension in “4D” is time, as available measurements are distributed over a given assimilation period. Therefore the least squares mechanism must be applied to a simulation over time that follows the time evolution model. This process gives a much better estimation of the initial state, because both position and time of measurements are taken into account. On the other hand, the adjoint problem involved is more complex, because it must run (backwards) over many time steps. This demanding application of AD justifies our efforts in reducing the runtime and memory costs of AD adjoint codes.

4.4 Linearization

Simulating a complex system often requires solving a system of Partial Differential Equations. This can be too expensive, in particular for real-time simulations. When one wants to simulate the reaction of this complex system to small perturbations around a fixed set of parameters, there is an efficient approximation: just suppose that the system is linear in a small neighborhood of the current set of parameters. The reaction of the system is thus approximated by a simple product of the variation of the parameters with the Jacobian matrix of the system. This Jacobian matrix can be obtained by AD. This is especially cheap when the Jacobian matrix is sparse. The simulation can be improved further by introducing higher-order derivatives, such as Taylor expansions, which can also be computed through AD. The result is often called a reduced model.

4.5 Mesh adaptation

Some approximation errors can be expressed by an adjoint state. Mesh adaptation can benefit from this. The classical optimization step can give an optimization direction not only for the control parameters, but also for the approximation parameters, and in particular the mesh geometry. The ultimate goal is to obtain optimal control parameters up to a precision prescribed in advance.

5.1 Impact of research results

Our research has an impact on environmental research: in Earth sciences, our gradients are used in inverse problems, to determine key properties in oceanography, glaciology, or climate models. For instance they determine basal friction coefficients of glaciers that are necessary to simulate their future evolution. Another example is to locate sources and sinks of CO2 by coupling atmospheric models and remote measurements.

6.1 New software

7.1 Profiling for improving Checkpointing schemes

Participants: Laurent Hascoët, Jean-Luc Bouchot, Shreyas Gaikwad [Univ. of Texas, Austin, USA], Sri Hari Krishna Narayanan [Argonne National Lab, Illinois, USA], Jan Hueckelheim [Argonne National Lab., Illinois, USA].

Data-Flow inversion is at the heart of the computation of gradients through AD. This amounts to providing (many of) the intermediate values computed at run-time, in reverse order. The bottleneck is the memory space needed to store these values before retrieving them in reverse order. Alternatively, these values may be recomputed when needed, in which case the bottleneck becomes a quadratic increase of run time. The classical answer is a memory/recomputation trade-off known as checkpointing. By applying checkpointing to a well-chosen collection of nested portions of the code, one can compute its gradient at reasonable memory and run-time costs. However, there is no general approach to find a good (let alone optimal) set of nested checkpoints.

A checkpoint can be placed on any closed sequence of code instructions, such as a procedure or any part of a procedure with a single entry location and a single exit location. The number of possible sets of nested checkpoints is immense and an exhaustive optimal search is therefore out of reach. Yet, we observe that performance of gradient evaluation strongly depends on the set of checkpoints. We observed factors up to 10 or more on large applications.

In order to iteratively improve performance of a gradient computation by changing the choice of checkpoints, we developed a run-time profiling mechanism. Based on a current selection of checkpoints, profiling can estimate the effect of removing each of the current checkpoints, in terms of run-time and memory gain or loss. This estimation is performed during one run of the gradient code, with a minimal overhead.

We implemented this profiling tool inside our AD tool Tapenade, and experimented on two large applications taken from the MIT-GCM test suites. We observed run-time gains up to a factor 4. This work 13 was presented at the 8th International Conference on AD, Chicago USA, September 2024.

7.2 Frontiers of the AD model

Participants: Laurent Hascoët, Jean-Luc Bouchot, Jan Hueckelheim [Argonne National Lab., Illinois, USA].

AD suffers from numerous limitations. Some limitations come from the constraints of application languages, or from coding styles adverse to AD or at least that make it inefficient. A crude distinction, debatable but still quite valid, can be made between AD by execution of a new transformed source code on one hand, and AD by delayed evaluation of an execution trace on the other hand. This distinction is all the more important for the reverse AD mode, that computes gradients.

Creating a new source code that computes the gradient requires a complex tool akin to a compiler, implying a costly development that depends of the targetted application language. However, the resulting new source code can be optimized at compile time, and its resulting performance is only limited by the unavoidable cost of data-flow inversion (see 7.1). On the other hand, an execution trace can be built by a relatively simple instrumentation of the original code, almost independently of the application language, be it heavily templated C++ or one of the newer popular dynamic languages. However, the resulting execution trace (or “tape”) is in general huge, as it contains not only the data needed for data-flow inversion, but also the full unrolled sequence of run-time instructions.

This year, we started to explore AD by source-transformation for a dynamic language such as Julia. Our goal is to explore, and hopefully lift, the restrictions that the constructs of Julia impose on source-transformation AD. We are still at a preliminary stage. Difficulties arise in particular from:

• the absence of explicit type declarations.
• the type structure and the special flavor of overloading known as “multiple dispatch”.
• the interpreted nature of the language, combined with hidden JIT compilation.
• the presence of macros that dynamically rewrite the source.

No differentiated code was produced yet, but a few test codes could be parsed and analyzed.

Other limitations of AD can be of a quite abstract nature, and may come for instance from the mathematical equations underlying the code, or from the fundamental difference between computer's float numbers and real numbers. Categorizing these limitations is difficult, and a (very long) catalogue may prove useless. Jan Hueckelheim considered the question of what one can reasonably expect from AD. The assumption is that problematic cases are often not about AD producing wrong derivatives, but rather meaningful derivatives, only for a model different from what the user has in mind. Accurate knowledge of the context in which AD derivatives are meaningful will help users build a realistic expectation for AD tools. A joint article “A taxonomy of automatic differentiation pitfalls” 11 was published this year.

7.3 Application to large industrial codes

Participants: Laurent Hascoët, Sébastien Bourasseau [ONERA], Cedric Content [ONERA], Bruno Maugars [ONERA], Shreyas Gaikwad [Univ. of Texas, Austin, USA], Sri Hari Krishna Narayanan [Argonne National Lab., Illinois, USA], Michael Vossbeck [The Inversion Lab, Hamburg, Germany].

We support users of Algorithmic Differentiation of large codes.

On CFD, we continue support for the use of Tapenade to provide gradient computations in the Onera Platform “SoNice”. SoNice is a new CFD platform developed at ONERA by Bourasseau, Maugars, Content and colleagues, as a successor to Elsa. In the modular architecture of SoNice, Tapenade is used to build the differentiated counterpart of each module or operator. The implementation of each module is devised to be platform-independent, eventually targetting several multithreaded architectures through e.g. OpenMP or Cuda. This imposes technical constraints on the language differentiated by Tapenade, at various abstraction levels that range from AD models for multithreaded code, down to ways of handling fpp and cpp directives and automatically setting entry points and labels in a differentiated code to allow for some necessary post-processing.

On Earth science, Shreyas Gaikwad continued building gradient computations on more test cases of the MIT-GCM, using Tapenade, with support from Krishna Narayanan from Argonne. These applications range from atmospheric to oceanic science and glaciology. This work is now published in  22. Also on Earth science, we support adjoint differentiation of the BEPS 29 code, a “biosphere” simulation model taking vegetation into account. This code is developed in part by the small company The Inversion Lab in Hamburg, Germany.

In Particle Physics, Krishna Narayanan differentiated with Tapenade the code HFBTHO from Lawrence Livermore National Lab., in tangent AD mode, which is a nuclear energy density functional (EDF) solver used to model the structure of atomic nuclei. This is a large Fortran code that unveiled a few technical issues but no major concern for Tapenade. An article is in preparation. We also successfully differentiated one test configuration of QCDNUM, a simulation code for Quantum Chromodynamics (QCD), in both tangent and reverse AD modes. This experiment, suggested by Lukas Heinrich and team at TU Munich and Max-Planck Institute, is supposed to lead to further collaboration.

7.4 Aeroacoustics/projet Norma

Participants: Alain Dervieux, Bastien Sauvage, Bruno Koobus [IMAG, Univ. of Montpellier], Stephen Wornom [IMAG, Univ. of Montpellier].

The progress in highly accurate schemes for compressible flows on unstructured meshes (together with advances in massive parallelization of these schemes) allows to solve problems previously out of reach, such as aeroacoustics around rotating machines. The four-years programme Norma, associating

• IMAG of Montpellier University (B. Koobus, coordinator),
• Ecuador of INRIA Sophia-Antipolis,

and supported by the ANR, was active till September 2024. Norma is a cooperation on the subject of extending Computational AeroAcoustics methods to simulate the noise emited by rotating machines (helicopters, aerial vehicles, unmanned aerial vehicles, wind turbines...). A final synthesis of the work is available as 30.

Since flows around rotating machines are turbulent and often characterized by laminar-turbulent transitions. The turbulence model must be able to take these phenomena into account while remaining reasonably expensive and of low dissipation in order to propagate acoustic waves accurately. The new turbulence model developed is an intermittency-based hybrid RANS/LES model (Reynolds averaged Navier-Stokes, Large Eddy Simulation) that addresses the targeted objectives. Flow simulation is based on the combination of an anisotropic mesh adaptation method with a Chimera or a multiple reference frame (MRF) method. On the other hand, and in order to improve the quality and efficiency of the prediction of unsteady flows, a new adaptation method based on a space-time metric is developed. Furthermore, a new adaptation technique, which introduces an adaptation criterion controlling in particular the LES error model, is also proposed for calculations that use hybrid turbulence models which are those favored in this program. Finally, a finite volume type numerical approximation scheme with quadratic or cubic reconstruction of the solution is developed in order to obtain high order accuracy on an unstructured mesh.

A detailed description with progress reports is available at this location.

7.5 Rotating machines

Participants: Alain Dervieux, Didier Chargy [Lemma, Sophia-Antipolis], Bastien Sauvage, Bruno Koobus [IMAG, Univ. of Montpellier].

An important output of the Norma project is the research of an efficient combination of multiple reference frame (MRF) rotating formulation with anisotropic mesh adaptation. A first version of this combination has been defined and validated by Bastien Sauvage. With this new method, Bastien Sauvage has finalised two unsteady mesh-adaptive computations, one of a single Caradonna-Tung helicoter rotor and one of the combination of the Caradonna-Tung rotor with the Robin fuselage (see Fig. 2). The computation of the single Caradonna-Tung rotor shows a well-formed vortex shedding at the end of the two rotor wings, corresponding to high-frequency sound emission.

Show image description

Computer-generated images and plots

Show image description

Computer-generated images and plots

7.6 Turbulence models

Participants: Bastien Sauvage, Alain Dervieux, Bruno Koobus [IMAG, Univ. of Montpellier], Stephen Wornom [IMAG, Univ. of Montpellier].

The prediction of academic and industrial turbulent flows progresses with each decade. For example in 21, most results were 2D, RANS computations were very far from mesh convergence, and far from experimental measurements. Also, they did not apply well to many unsteady flows. Since then, new VLES (Very Large Eddy Simulation) and hybrid models appeared for addressing a large class of unsteady flows. At the beginning of 2000's, a first generation of VLES/hybrid methods, including the Detached Eddy Simulation, showed interesting results. It is interesting to measure how these new physical models, and new numerical methods, improved one or two decades later. In association with IMAG, a wide series of test cases was recomputed in order to measure on these cases the progress in turbulence computation obtained thanks to the three novelties introduced by the Montpellier-Sophia cooperation:

• a novel hybrid LES-RANS model with intermittency,
• an fourth-order CENO4 advective approximation for RANS and hybrid calculations,
• the new unsteady mesh adaptation for RANS and hybrid calculations.

An article in preparation ("Computing the flow past a cylinder : influence of models and numerics" by B. Sauvage, F. Miralles, S. Wornom, B. Koobus, A. Dervieux) discusses and contrasts these simulations.

7.7 Space-time mesh adaptation

Participants: Bastien Sauvage, Alain Dervieux, Frédéric Alauzet [GammaO, INRIA, Saclay].

The INRIA teams GammaO (Saclay) and Ecuador (Sophia-Antipolis) have continued to study the application of anisotropic mesh adaptation to unsteady flow simulation. The baseline approach is the Global Transient Fixed Point algorithm combined with a timestep relying on Courant-type stability condition for explicit time-advancing. This remains the best approach for many transient flows. For many unsteady turbulent flows at high Reynolds number, this is however inefficient since very small cells in the boundary layer impose a very small explicit time step. Implicit timestepping is compulsory. Indeed, the time steps which can be used are notably larger than those permitted with an explicit time advancing. Large time steps bring a higher CPU efficiency, but the time approximation accuracy becomes an issue. Too large time steps degrade the prediction, too small time steps increases the computational cost. We developed a novel space and time adaptation method for the implicit time advancing used in turbulence computations. The new method has been extended to a new Global Transient Fixed Point mesh adaptation algorithm addressing turbulent flows with several meshes applied to the time interval. This work has been published in 12.

7.8 Mesh adaptation for LES

Participants: Bastien Sauvage, Alain Dervieux, Bruno Koobus [IMAG, Univ. of Montpellier], Frédéric Alauzet [GammaO, INRIA, Saclay].

With statistical turbulence models, only a part of turbulent industrial flows can be predicted at an affordable cost. The rest may involve large detached flow regions, which cannot be accurately described by statistical modeling, or vortices producing noise, that the engineer wants to predict accurately. The Large Eddy Simulation (LES) is a model which predicts a part of the vortices of industrial interest. LES relies on filtering too small vortices and on modeling their effect on the larger ones. But this approach is one or two orders of magnitude more computer intensive than statistical modeling and therefore cannot be routinely used by engineers. Germano proposed an analysis using two different filters in order to measure the efficicency of a family of LES models. Recently, Toosi and Larsson demonstrated that the Germano analysis in fact deals with the source term of LES modeling error. We propose a novel adaptation method based on the Germano dynamic-LES analysis, taking into account the LES model error. This method was validated on a set of test cases and exhibits a better efficiency. An article is being prepared ("A metric-based mesh adaptation for hybrid RANS/LES flow calculations" by B. Sauvage, B. Koobus, F. Alauzet, A. Dervieux).

8.1 International research visitors

9.1 Promoting scientific activities

9.2 Teaching - Supervision - Juries

10.1 Major publications

• 1 articleF.F. Courty, A.A. Dervieux, B.B. Koobus and L.L. Hascoët. Reverse automatic differentiation for optimum design: from adjoint state assembly to gradient computation.Optimization Methods and Software1852003, 615-627
• 2 inproceedingsB.B. Dauvergne and L.L. Hascoët. The Data-Flow Equations of Checkpointing in reverse Automatic Differentiation.International Conference on Computational Science, ICCS 2006, Reading, UK2006
• 3 articleD.Daniel Goldberg, S. H.Sri Hari Krishna Narayanan, L.Laurent Hascoët and J.Jean Utke. An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem.Geoscientific Model Development952016, 27HAL
• 4 incollectionL.L. Hascoët. Adjoints by Automatic Differentiation.Advanced data assimilation for geosciencesOxford University Press2014, URL: https://hal.inria.fr/hal-01109881back to text
• 5 articleL.L. Hascoët, U.U. Naumann and V.V. Pascual. ``To Be Recorded'' Analysis in Reverse-Mode Automatic Differentiation.Future Generation Computer Systems2182004
• 6 articleL.L. Hascoët and V.V. Pascual. The Tapenade Automatic Differentiation tool: Principles, Model, and Specification.ACM Transactions On Mathematical Software3932013, URL: http://dx.doi.org/10.1145/2450153.2450158
• 7 articleL.L. Hascoët, J.J. Utke and U.U. Naumann. Cheaper Adjoints by Reversing Address Computations.Scientific Programming1612008, 81--92
• 8 articleL.Laurent Hascoët and J.Jean Utke. Programming language features, usage patterns, and the efficiency of generated adjoint code.Optimization Methods and Software312016, 885--903HALDOI
• 9 articleL.L. Hascoët, M.M. Vázquez, B.B. Koobus and A.A. Dervieux. A Framework for Adjoint-based Shape Design and Error Control.Computational Fluid Dynamics Journal1642008, 454-464
• 10 articleJ. C.Jan Christian Hueckelheim, L.Laurent Hascoët and J.-D.Jens-Dominik Müller. Algorithmic differentiation of code with multiple context-specific activities.ACM Transactions on Mathematical Software2016HAL

10.2 Publications of the year

10.3 Cited publications

• 15 bookA.A. Aho, R.R. Sethi and J.J. Ullman. Compilers: Principles, Techniques and Tools.Addison-Wesley1986back to text
• 16 techreportI.I. Attali, V.V. Pascual and C.C. Roudet. A language and an integrated environment for program transformations.3313INRIA1997, URL: http://hal.inria.fr/inria-00073376back to text
• 17 articleB.B. Christianson. Reverse accumulation and implicit functions.Optimization Methods and Software941998, 307--322back to text
• 18 articleD.D. Clément, J.J. Despeyroux, L.L. Hascoët and G.G. Kahn. Natural semantics on the computer.Proceedings, France-Japan AI and CS Symposium, ICOTAlso, Information Processing Society of Japan, Technical Memorandum PL-86-6. Also INRIA research report # 4161986, 49-89URL: http://hal.inria.fr/inria-00076140back to text
• 19 articleP.P. Cousot. Abstract Interpretation.ACM Computing Surveys2811996, 324-328back to text
• 20 articleB.B. Creusillet and F.F. Irigoin. Interprocedural Array Region Analyses.International Journal of Parallel Programming2461996, 513--546back to text
• 21 bookA.A. Dervieux, M.M. Braza and J.-P.J.-P. Dussauge. Computation and comparison of efficient turbulence models for Aeronautics - European Research Project ETMA.Notes on Numerical Fluid Mechanics65Vieweg, Braunschweig; Wiesbaden1998back to text
• 22 articleS.S. Gaikwad, S.-H.S.-H.-K. Narayanan, L.L. Hascoët, J.-M.J.-M. Campin, H.H. Pillar, A.A. Nguyen, J.J. Hüeckelheim, P.P. Hovland and P.P. Heimbach. MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade.Future Generation Computer Systems1632015back to text
• 23 articleJ.J.C. Gilbert. Automatic differentiation and iterative processes.Optimization Methods and Software11992, 13--21back to text
• 24 inproceedingsM.-B.M.-B. Giles. Adjoint methods for aeronautical design.Proceedings of the ECCOMAS CFD ConferenceSwansea, U.K.2001back to textback to text
• 25 articleA.A. Griewank and C.C. Faure. Reduced Gradients and Hessians from Fixed Point Iteration for State Equations.Numerical Algorithms30(2)2002, 113--139back to text
• 26 bookA.A. Griewank and A.A. Walther. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation.SIAM, Other Titles in Applied Mathematics2008back to text
• 27 phdthesisL.L. Hascoët. Transformations automatiques de spécifications sémantiques: application: Un vérificateur de types incremental.Université de Nice Sophia-Antipolis1987back to text
• 28 techreportP.P. Hovland, B.B. Mohammadi and C.C. Bischof. Automatic Differentiation of Navier-Stokes computations.MCS-P687-0997Argonne National Laboratory1997back to text
• 29 articleW.W.M. Ju, J.J.M. Chen, T.T.A. Black, A.A.G. Barr, J.J. Liu and B.B.Z. Chen. Modelling multi-year coupled carbon and water fluxes in a boreal aspen forest.Agric. For. Meteorol.1401-42006, 136--151DOIback to text
• 30 techreportB.B. Koobus. Compte-rendu de fin de projet, Projet NORMA.ANR-19-CE40-0020-01, Programme AAPG 20192024back to text
• 31 articleE.E. Larour, J.J. Utke, B.B. Csatho, A.A. Schenk, H.H. Seroussi, M.M. Morlighem, E.E. Rignot, N.N. Schlegel and A.A. Khazendar. Inferred basal friction and surface mass balance of the Northeast Greenland Ice Stream using data assimilation of ICESat (Ice Cloud and land Elevation Satellite) surface altimetry and ISSM (Ice Sheet System Model).Cryosphere862014, 2335-2351URL: http://www.the-cryosphere.net/8/2335/2014/DOIback to text
• 32 articleF.-X.F.-X. Le Dimet and O.O. Talagrand. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects.Tellus38A1986, 97-110back to textback to text
• 33 articleB.B. Mohammadi. Practical application to fluid flows of automatic differentiation for design problems.Von Karman Lecture Series1997back to text
• 34 phdthesisN.N. Rostaing. Différentiation Automatique: application à un problème d'optimisation en météorologie.université de Nice Sophia-Antipolis1993back to text
• 35 inproceedingsR.R. Rugina and M.M. Rinard. Symbolic Bounds Analysis of Pointers, Array Indices, and Accessed Memory Regions.Proceedings of the ACM SIGPLAN'00 Conference on Programming Language Design and ImplementationACM2000back to text