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Variational Inference Using a Differentiable Multigrid Linear Solver
Authors:
Andrés Ramírez,
Philipp Haim,
David Föger,
Torsten A. Enßlin,
Philipp Frank,
Philipp Gschwandtner,
Dominik Jüstel,
Philipp Mertsch,
Vo Hong Minh Phan,
Laurin Söding,
Hanieh Zandinejad,
Ralf Kissmann
Abstract:
Gradient-based Bayesian inference methods require efficient access to Jacobian and adjoint-Jacobian operators of high-dimensional forward models. While multigrid solvers provide near-optimal complexity for elliptic partial differential equations, they are rarely available in forms compatible with automatic differentiation (AD). We develop a differentiable multigrid solver for steady-state diffusio…
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Gradient-based Bayesian inference methods require efficient access to Jacobian and adjoint-Jacobian operators of high-dimensional forward models. While multigrid solvers provide near-optimal complexity for elliptic partial differential equations, they are rarely available in forms compatible with automatic differentiation (AD). We develop a differentiable multigrid solver for steady-state diffusion-absorption problems and derive its adjoint operations analytically through the full multigrid hierarchy. The resulting solver, DMGS, is implemented in C++ and interfaced with JAX to provide efficient Jacobian-vector and vector-Jacobian products for variational inference in the NIFTy framework. We validate the approach on a 3D inverse problem involving diffuse radiative transfer in tissue, reconstructing an effective radiative source from Monte Carlo-simulated data. The reconstruction reproduces the data at a reduced chi-squared of 1.1 and generalizes to 32 independent validation datasets. Benchmarks against a JAX-native multigrid implementation show comparable runtimes and consistently lower peak memory for the hand-derived adjoint, with modest reverse-mode overhead. These results establish differentiable multigrid solvers as practical building blocks for variational inference in PDE-constrained problems.
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Submitted 1 August, 2026;
originally announced August 2026.
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Conditioning Deep Anatomical Prior Knowledge for Reconstruction of Multispectral Optoacoustic Tomography Images
Authors:
Sarah Franceschin,
Lukas Imanuel Scheel-Platz,
Philipp Haim,
Guillaume Zahnd,
Vasilis Ntziachristos,
Dominik Jüstel
Abstract:
Accurately delineating tissues and reconstructing their chromophore compositions from Multispectral Optoacoustic Tomography (MSOT) images is a key challenge in optoacoustic imaging. The difficulty arises because light fluence distributions within tissue intrinsically depend on spectral optical properties, making the inverse problem inherently ill-posed. Currently, there is a lack of studies levera…
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Accurately delineating tissues and reconstructing their chromophore compositions from Multispectral Optoacoustic Tomography (MSOT) images is a key challenge in optoacoustic imaging. The difficulty arises because light fluence distributions within tissue intrinsically depend on spectral optical properties, making the inverse problem inherently ill-posed. Currently, there is a lack of studies leveraging a priori probabilistic anatomical knowledge to guide tissue segmentation and infer chromophore composition. Moreover, most current studies address these two tasks sequentially, which can result in errors accumulating. through the process. To address these issues, we present Anatomical Priors for Reconstruction of Optoacoustic Tomography (APRECOT), a method that leverages probabilistic models of anatomical structures and tissue properties, to enable simultaneous segmentation of tissues and reconstruction of their bulk chromophore compositions. In this proof-of-concept using in-silico data, we show that incorporating probabilistic anatomical context strongly improves the accuracy of bulk chromophore concentration estimation compared to reference methods that do not use any anatomical context or use sequential strategies. This work represents an essential step towards an MSOT imaging mode that directly provides clinically relevant information, such as imaging tissue oxygenation dynamics or disease-related changes in tissue composition.
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Submitted 15 June, 2026;
originally announced June 2026.
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DeepLight: A Sobolev-trained Image-to-Image Surrogate Model for Light Transport in Tissue
Authors:
Philipp Haim,
Vasilis Ntziachristos,
Torsten Enßlin,
Dominik Jüstel
Abstract:
In optoacoustic imaging, recovering the absorption coefficients of tissue by inverting the light transport remains a challenging problem. Improvements in solving this problem can greatly benefit the clinical value of optoacoustic imaging. Existing variational inversion methods require an accurate and differentiable model of this light transport. As neural surrogate models allow fast and differenti…
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In optoacoustic imaging, recovering the absorption coefficients of tissue by inverting the light transport remains a challenging problem. Improvements in solving this problem can greatly benefit the clinical value of optoacoustic imaging. Existing variational inversion methods require an accurate and differentiable model of this light transport. As neural surrogate models allow fast and differentiable simulations of complex physical processes, they are considered promising candidates to be used in solving such inverse problems. However, there are in general no guarantees that the derivatives of these surrogate models accurately match those of the underlying physical operator. As accurate derivatives are central to solving inverse problems, errors in the model derivative can considerably hinder high fidelity reconstructions. To overcome this limitation, we present a surrogate model for light transport in tissue that uses Sobolev training to improve the accuracy of the model derivatives. Additionally, the form of Sobolev training we used is suitable for high-dimensional models in general. Our results demonstrate that Sobolev training for a light transport surrogate model not only improves derivative accuracy but also reduces generalization error for in-distribution and out-of-distribution samples. These improvements promise to considerably enhance the utility of the surrogate model in downstream tasks, especially in solving inverse problems.
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Submitted 14 January, 2026;
originally announced January 2026.
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A Method for Accurate Spatial Focusing Simulation via Numerical Integration and its Application in Optoacoustic Tomography
Authors:
Maximilian Bader,
Philipp Haim,
Lukas Imanuel Scheel-Platz,
Angelos Karlas,
Hedwig Irl,
Vasilis Ntziachristos,
Dominik Jüstel
Abstract:
The spatial sensitivity of an ultrasound transducer, which strongly influences its suitability for different applications, depends on the shape of the transducer surface. Accurate simulation of these spatial effects is important for transducer characterization and design, and for system response modelling in imaging applications. In optoacoustic imaging, broadband transducers are used to capitaliz…
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The spatial sensitivity of an ultrasound transducer, which strongly influences its suitability for different applications, depends on the shape of the transducer surface. Accurate simulation of these spatial effects is important for transducer characterization and design, and for system response modelling in imaging applications. In optoacoustic imaging, broadband transducers are used to capitalize on the rich frequency content of the signals, but their usage makes highly accurate simulations with general wave equation solvers prohibitively memory- and time-intensive. Therefore, specialized tools for simulating the isolated spatial focusing properties described by the spatial impulse response (SIR) have been developed. However, the challenging numerics of the SIR and the necessity to convolve the SIR with the wave shape generated by the optoacoustic absorber to simulate the system response lead to numerical inaccuracies of SIR-based methods. In addition, the approximation error of these methods cannot be controlled a priori. To circumvent the problems associated with the explicit calculation of SIR, we propose directly computing the convolution of the required wave shape with the SIR, which we call the spatial pulse response (SPR). We demonstrate that by utilizing an h-adaptive cubature algorithm, SPR can be computed with significantly higher accuracy than an SIR-based reference method, and the approximation error can be controlled with a tolerance parameter. In addition, the integration of accurate SPR simulations into model-based optoacoustic image reconstruction is shown to improve image contrast and reduce noise artifacts. Precise system characterization and simulation leads to improved imaging performance, ultimately increasing the value of optoacoustic imaging systems for clinical applications.
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Submitted 16 September, 2024;
originally announced September 2024.