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<title>tlm_adjoint — tlm_adjoint documentation</title>
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<section id="tlm-adjoint">
<h1>tlm_adjoint<a class="headerlink" href="#tlm-adjoint" title="Link to this heading"></a></h1>
<p>tlm_adjoint is a high-level algorithmic differentiation tool, principally for
use with <a class="reference external" href="https://firedrakeproject.org">Firedrake</a>.</p>
<p>The primary aim of tlm_adjoint is to enable higher order adjoint calculations
– and in particular to compute Hessian information – while also using adjoint
checkpointing schedules, and allowing for caching of assembled finite element
data, and caching of linear solver data.</p>
<section id="features">
<h2>Features<a class="headerlink" href="#features" title="Link to this heading"></a></h2>
<blockquote>
<div><ul class="simple">
<li><p>Integrates with the Firedrake automated code generation library, and
applies a high-level algorithmic differentiation approach to enable
tangent-linear and adjoint calculations.</p></li>
<li><p>Applies a <em>reverse-over-multiple-forward</em> approach for higher order
adjoint calculations. For example a Hessian action on some given
direction is computed by deriving an adjoint associated with a combined
forward/tangent-linear calculation.</p></li>
<li><p>Implements adjoint checkpointing schedules to enable large problems to
be tackled.</p></li>
<li><p>Can apply automated finite element assembly and linear solver caching.
Cached data can be reused across the forward, tangent-linear, and adjoint
calculations.</p></li>
<li><p>Provides a simple ‘escape-hatch’ to enable parts of the problem, not
otherwise supported by tlm_adjoint or the backend library, to be added,
with adjoint or tangent-linear information defined manually.</p></li>
</ul>
</div></blockquote>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h2>
<p>The following Jupyter notebooks introduce derivative calculations using
tlm_adjoint.</p>
<ul class="simple">
<li><p><a class="reference internal" href="examples/0_getting_started.html"><span class="doc">Getting started with tlm_adjoint</span></a>:
Introduces derivative calculations using tlm_adjoint.</p></li>
<li><p><a class="reference internal" href="examples/1_time_independent.html"><span class="doc">Time-independent example</span></a>: An example
including the solution of a time-independent partial differential equation
using Firedrake.</p></li>
<li><p><a class="reference internal" href="examples/2_verification.html"><span class="doc">Verifying derivative calculations</span></a>:
Introduces Taylor remainder convergence testing.</p></li>
<li><p><a class="reference internal" href="examples/3_time_dependent.html"><span class="doc">Time-dependent example</span></a>: An example
including the solution of a time-dependent partial differential equation
using Firedrake. Introduces checkpointing.</p></li>
<li><p><a class="reference internal" href="examples/4_riesz_maps.html"><span class="doc">Visualizing derivatives</span></a>: The use of a Riesz
map to visualize the result of differentiating with respect to a finite
element discretized function using the adjoint method.</p></li>
<li><p><a class="reference internal" href="examples/5_optimization.html"><span class="doc">Functional minimization</span></a>: The solution of
partial differential equation constrained optimization problems.</p></li>
<li><p><a class="reference internal" href="examples/6_custom_operations.html"><span class="doc">Defining custom operations</span></a>: An
example using the tlm_adjoint ‘escape-hatch’ to define a custom operation.</p></li>
<li><p><a class="reference internal" href="examples/7_jax_integration.html"><span class="doc">JAX integration</span></a>: A finite difference
example using JAX.</p></li>
</ul>
</section>
<section id="advanced-tutorials">
<h2>Advanced tutorials<a class="headerlink" href="#advanced-tutorials" title="Link to this heading"></a></h2>
<ul class="simple">
<li><p><a class="reference internal" href="examples/8_hessian_uq.html"><span class="doc">Hessian-based uncertainty quantification</span></a></p></li>
</ul>
</section>
<section id="source-and-license">
<h2>Source and license<a class="headerlink" href="#source-and-license" title="Link to this heading"></a></h2>
<p>The source code is available from the
<a class="reference external" href="https://github.com/tlm-adjoint/tlm_adjoint">tlm_adjoint GitHub repository</a>.
tlm_adjoint is licensed under the GNU LGPL version 3.</p>
</section>
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<h2>Indices<a class="headerlink" href="#indices" title="Link to this heading"></a></h2>
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<li><p><a class="reference internal" href="py-modindex.html"><span class="std std-ref">Module Index</span></a></p></li>
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