SGN: Sparse Gauss-Newton for Accelerated Sensitivity Analysis

Algorithms at the intersection of computer graphics and medicine have recently gained renewed attention. A particular interest are methods for virtual surgery planning (VSP), where treatment parameters must be carefully chosen to achieve a desired treatment outcome. FEM simulators can verify the treatment parameters by comparing a predicted outcome to the desired one. However, estimating the optimal parameters amounts to solving a challenging inverse problem. In current clinical practice it is solved manually by surgeons, who rely on their experience and intuition to iteratively refine the parameters, verifying them with simulated predictions. We prototype a differentiable FEM simulator and explore how it can enhance and simplify treatment planning, which is ultimately necessary to integrate simulation-based VSP tools into a clinical workflow. Specifically, we define a parametric treatment model based on surgeon input, and with analytically derived simulation gradients we optimise it against an objective defined on the visible facial 3D surface. By using sensitivity analysis, we can easily explore the solution-space with first-order approximations, which allow the surgeon to interactively visualise the effect of parameter variations on a given treatment plan. The objective function allows landmarks to be freely chosen, accommodating the multiple methodologies in clinical planning. We show that even with a very sparse set of guiding landmarks, our simulator robustly converges to a feasible post-treatment shape.

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“…We solve this problem using a Sparse Gauss‐Newton solver [ZCT22]. Using this technique, the problem is reduced to solving the sparse system

…”

Section: Methodsmentioning

confidence: 99%

“…Developing an automatic method to optimise the treatment plan from a given target promises to simplify the way the tool is used in practice. Differentiable simulation offers a methodology for solving such problems, with many recent examples in graphics and robotics [IKKP17,KK19,SWR*21,HHD*21, ZKBT17,ZCT22].…”

Section: Introductionmentioning

confidence: 99%

Differentiable Simulation for Outcome‐Driven Orthognathic Surgery Planning

Dorda

Peter

Borer

et al. 2022

Computer Graphics Forum

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“…[CS21; ZLZ*21] further verified various network models with classical tasks. [ZLCT21] proposed the converse density space objective, which applies the step‐wise predicted structure to guide the network fitting.…”

Section: Related Workmentioning

confidence: 99%

“…Second, the optimization convergence was unsatisfactory, as hundreds of iterations were required for a classic benchmark task [ZLZ*21] (Messerschmitt‐Bölkow‐Blohm beam), while conventional explicit methods cost dozens of iterations [HX07; FS20]. Although several studies have demonstrated exciting progress, such as with the mesh‐independent FEA solver (still tradeoff with the computation time) [ZLCT21], the overall effects are doubted due to the deficiency in the verification and comparison of the optimization‐performance under complex tasks.…”

Section: Related Workmentioning

confidence: 99%

NSTO: Neural Synthesizing Topology Optimization for Modulated Structure Generation

Zhong

Punpongsanon

Iwai

et al. 2022

Computer Graphics Forum

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Nature evolves structures like honeycombs at optimized performance with limited material. These efficient structures can be artificially created with the collaboration of structural topology optimization and additive manufacturing. However, the extensive computation cost of topology optimization causes low mesh resolution, long solving time, and rough boundaries that fail to match the requirements for meeting the growing personal fabrication demands and printing capability. Therefore, we propose the neural synthesizing topology optimization that leverages a self‐supervised coordinate‐based network to optimize structures with significantly shorter computation time, where the network encodes the structural material layout as an implicit function of coordinates. Continuous solution space is further generated from optimization tasks under varying boundary conditions or constraints for users' instant inference of novel solutions. We demonstrate the system's efficacy for a broad usage scenario through numerical experiments and 3D printing.

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“…We describe the system dynamics as a function of a control input vector evolving over a time horizon and a time-invariant set of footholds. We solve the resulting OCP using a second-order numerical solver [8] that leverages sensitivity analysis (SA) [9,10,11,12] to compute the exact values of the required derivatives efficiently. This approach significantly improves the robustness of the controller while ensuring real-time execution.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Model Predictive Control for Quadrupedal Locomotion Using Second-Order Sensitivity Analysis

Kang¹,

Vincenti²,

Coros³

2022

Preprint

Self Cite

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We present a versatile nonlinear model predictive control (NMPC) formulation for quadrupedal locomotion. Our formulation jointly optimizes a base trajectory and a set of footholds over a finite time horizon based on simplified dynamics models. We leverage second-order sensitivity analysis and a sparse Gauss-Newton (SGN) method to solve the resulting optimal control problems. We further describe our ongoing effort to verify our approach through simulation and hardware experiments. Finally, we extend our locomotion framework to deal with challenging tasks that comprise gap crossing, movement on stepping stones, and multi-robot control.

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SGN: Sparse Gauss-Newton for Accelerated Sensitivity Analysis

Cited by 10 publications

References 45 publications

Differentiable Simulation for Outcome‐Driven Orthognathic Surgery Planning

Differentiable Simulation for Outcome‐Driven Orthognathic Surgery Planning

NSTO: Neural Synthesizing Topology Optimization for Modulated Structure Generation

Nonlinear Model Predictive Control for Quadrupedal Locomotion Using Second-Order Sensitivity Analysis

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