A parallel-in-time approach for accelerating direct-adjoint studies

Skene, Calum S.; Eggl, Maximilian F.; Schmid, Peter J.

doi:10.1016/j.jcp.2020.110033

Cited by 5 publications

(2 citation statements)

References 47 publications

(78 reference statements)

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“…Thus, the cost function needs to be rewritten to reflect the discontinuity as follows where is the spine response at snapshot t . The iterative scheme we chose to employ is a gradient-based adjoint approach (Jameson, 1988, or Skene et al, 2021). The adjoint method was chosen, in part, due to its ability to easily and efficiently handle multiple simultaneous optimisation parameters.…”

Section: Methodsmentioning

confidence: 99%

A quantitative rule to explain multi-spine plasticity

Chater

Eggl

Goda

et al. 2022

Preprint

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Neurons receive thousands of inputs onto their dendritic arbour, where individual synapses undergo activity-dependent changes in strength. The durable forms of synaptic strength change, long-term potentiation (LTP) and long-term depression (LTD), require calcium entry through N-methyl-D-aspartate receptors (NMDARs) that triggers downstream protein signalling cascades in the dendrite. Intriguingly, sLTP and sLTD are not necessarily restricted to the active, targeted synapses (homosynapses), and the changes in synaptic strength can spread and affect the strengths of inactive or non-stimulated synapses (heterosynapses) on the same cell. Precisely how neurons allocate resources for implementing the changes in strength at individual synapses depending on their proximity to activity across space and time remains an open question. In order to gain insights into the elementary processes underlying heterosynaptic plasticity and their interplay with homosynaptic plasticity, we have combined experimental and mathematical modelling approaches. On the one hand, we used glutamate uncaging to precisely and systematically stimulate variable numbers of homosynapses sharing the same dendritic branch whilst monitoring tens of other heterosynapses on the same dendrite. Homosynaptic potentiation of clusters of dendritic spines leads to heterosynaptic changes that are NMDAR-dependent, requiring CaMKII and calcineurin activity. On the other hand, inspired by the calcium levels hypothesis where different amounts of calcium lead to either growth or shrinkage of spines, we have built a model based on a dual-role calcium-dependent protein that induces spine shrinkage or potentiation dynamics. Comparing our experimental results with model predictions, we find that (i) both collaboration and competition among spines for protein resources are key drivers of heterosynaptic plasticity and (ii) the temporal and spatial distance between simultaneously stimulated spines impact the resulting spine dynamics. Moreover, our model can reconcile a number of disparate and sometimes contradictory experimental reports of heterosynaptic sLTP or sLTD at homo and heterosynaptic spines. Our results provide a quantitative description of the heterosynaptic footprint unfolding across minutes and hours post-stimulation across tens of microns of dendritic space. This broadens our knowledge about the operation of non-linear dendritic summation rules and how they impact spiking decisions.

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Section: Methodsmentioning

confidence: 99%

A quantitative rule to explain multi-spine plasticity

Chater

Eggl

Goda

et al. 2022

Preprint

Self Cite

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“…Leveraging these techniques enables the construction of algorithms for optimal control which scale well in parallel when increasing the amount of work in the time dimension. Some parallel-in-time approaches for the optimal-control problem (1.1) use the direct-adjoint optimization loop [14,28], where all embedded ivp solves are tackled using time-parallel methods such as pfasst [7] or the well-known Parareal algorithm [20]. Others use the system (1.3); an example is ParaOpt [10], inspired by Parareal.…”

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confidence: 99%

On Generalized Preconditioners for Time-Parallel Parabolic Optimal Control

Bouillon,

Samaey,

Meerbergen

2024

SIAM J. Sci. Comput.

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The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control of linear parabolic pdes, the state-of-the-art ParaDiag method is limited to solving self-adjoint problems with a tracking objective. We propose three improvements to the ParaDiag method: the use of alpha-circulant matrices to construct an alternative preconditioner, a generalization of the algorithm for solving non-self-adjoint equations, and the formulation of an algorithm for terminal-cost objectives. We present novel analytic results about the eigenvalues of the preconditioned systems for all discussed ParaDiag algorithms in the case of self-adjoint equations, which proves the favorable properties the alpha-circulant preconditioner. We use these results to perform a theoretical parallelscaling analysis of ParaDiag for self-adjoint problems. Numerical tests confirm our findings and suggest that the self-adjoint behavior, which is backed by theory, generalizes to the non-self-adjoint case. We provide a sequential, open-source reference solver in Matlab for all discussed algorithms.

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