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arxiv: 2606.28600 · v1 · pith:6MFAZUISnew · submitted 2026-06-26 · 💻 cs.NE · cs.AI· cs.LG· cs.SY· eess.SY

Neuromorphic Energy-Aware Learning for Adaptive Deep Brain Stimulation

Binh Nguyen , Colleen Josephson , Mircea Teodorescu , Gert Cauwenberghs , Jason Eshraghian This is my paper

Pith reviewed 2026-06-30 00:50 UTC · model grok-4.3

classification 💻 cs.NE cs.AIcs.LGcs.SYeess.SY
keywords deep brain stimulationneuromorphic computingreinforcement learningParkinson's diseasespiking neural networksenergy efficiencyclosed-loop controladaptive stimulation
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The pith

Energy-aware learning trains a spiking Q-network to cut DBS charge by 80% while suppressing alpha-beta oscillations by 45.2%.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that adding the energy cost of stimulation directly into the reinforcement learning reward produces a deep spiking Q-network policy that suppresses pathological oscillations in a biophysical brain circuit model. This policy achieves 45.2% reduction in alpha-beta oscillations while delivering 80% less charge than continuous deep brain stimulation. The resulting controller is then compressed through sparsity-constrained knowledge distillation and deployed on a neuromorphic processor that consumes 0.52 mW. The work therefore treats both the stimulation actuator and the inference engine as first-class energy costs that must be co-optimized for implantable neuromodulation.

Core claim

Incorporating actuator energy into the reward of a reinforcement learning agent allows a deep spiking Q-network, trained inside a cortico-basal ganglia-thalamic circuit model, to learn an adaptive deep brain stimulation policy that reduces pathological alpha-beta oscillations by 45.2% while cutting stimulation charge by 80.0% relative to continuous DBS; the policy can then be compressed onto the SynSense XyloAudio 3 neuromorphic processor at 0.52 mW inference power, yielding 28.1 times lower energy per inference than an equivalent artificial neural network on conventional hardware.

What carries the argument

Energy-aware reinforcement learning reward that penalizes stimulation charge, implemented inside a deep spiking Q-network and followed by sparsity-constrained knowledge distillation to a neuromorphic processor.

If this is right

  • Adaptive DBS policies can achieve substantial oscillation suppression at far lower stimulation energy than continuous delivery.
  • Neuromorphic hardware can host the resulting policies at sub-milliwatt inference power.
  • Co-optimization of controller and actuator energy addresses both dominant power demands in implantable neuromodulation devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reward-augmentation approach could be tested in other closed-loop neuromodulation settings such as epilepsy or pain management.
  • Real deployment would require checking whether the learned policy remains effective when the underlying circuit model is replaced by patient-specific data.
  • The method may generalize to any physical system in which actuator energy dominates total consumption once inference is already efficient.

Load-bearing premise

The biophysical cortico-basal ganglia-thalamic circuit model accurately represents the dynamics of pathological oscillations and the effects of stimulation in actual human patients.

What would settle it

Application of the learned stimulation policy to human patients or a higher-fidelity model, with direct measurement of both oscillation suppression and total delivered charge compared against continuous DBS.

Figures

Figures reproduced from arXiv: 2606.28600 by Binh Nguyen, Colleen Josephson, Gert Cauwenberghs, Jason Eshraghian, Mircea Teodorescu.

Figure 1
Figure 1. Figure 1: Signal representation: conventional versus neuromorphic. (A) Raw brain signals from the CBGT model. Top: A sample continuous membrane potential trace demonstrating spike generation via threshold crossing (−20 mV). Bottom: The resulting 80-channel spike raster across eight basal ganglia populations (TH, STN, GPe, GPi, Str-D2, Str-D1, Cor-E, Cor-I). (B) Conventional window-aggregated processing collapses the… view at source ↗
Figure 2
Figure 2. Figure 2: Neuromorphic closed-loop DBS framework. (A) Pathological β oscillations in the parkinsonian basal ganglia circuit targeted by DBS. (B) A spiking RL controller (DSQN) modulates DBS parameters in a closed loop with a biophysical CBGT model. (C) Sparsity-constrained distil￾lation compresses the teacher SNN into sparse students, trading synaptic operations (SynOps) for therapeutic efficacy. (D) Hardware deploy… view at source ↗
Figure 3
Figure 3. Figure 3: Therapeutic efficacy of the neuromorphic controller. (A1–A2) Time-frequency spec￾trograms of GPi population spiking activity (short-time Fourier spectrogram, representative seed). The unstimulated state (A1) shows persistent high-power activation in the α-β band (7–35 Hz, white dashed lines); the SNN closed-loop state (A2) shows rapid suppression of this pathological synchro￾nization. (B) Multi-taper power… view at source ↗
Figure 4
Figure 4. Figure 4: Energy-aware stimulation comparison across alternating healthy and parkinsonian states. (A) GPi β-band power across six conditions: unstimulated (dark navy), continuous DBS (grey), clinical dual-threshold aDBS (green), ANN baseline (orange), RNN baseline (purple), and the adaptive SNN controller (blue). Light pink shading indicates parkinsonian (PD) blocks. The horizontal dotted line marks the therapeutic … view at source ↗
Figure 5
Figure 5. Figure 5: Energy–Efficacy Trade-off in Sparsity-Constrained Distillation. (A) Heatmap of multi￾taper α-β band power reduction (same metric as [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Hardware benchmark comparison of neuromorphic (Xylo Audio 3) versus edge AI (Jetson Orin Nano CUDA) implementations. (A) Inference latency. (B) Power consumption. (C) Energy per inference. The Xylo-deployed SNN consumes 28.1× less energy per inference than the ANN and 72.5× less than the RNN on the Jetson, despite being ∼390× slower, because of its ∼11,000× lower power draw. in the parkinsonian state Littl… view at source ↗
read the original abstract

Neuromorphic and edge computing research has focused on reducing the inference cost of neural network controllers, yet in physical closed-loop systems the actuator can rival or exceed an efficient controller in energy. An efficient controller is therefore necessary but not sufficient, because the actuator becomes the cost worth reducing once inference no longer dominates it. Here, we introduce energy-aware learning, an approach that incorporates actuator energy directly into the reinforcement learning reward, and demonstrate it in closed-loop deep brain stimulation (DBS) for Parkinson's disease. A deep spiking Q-network, trained in a biophysical cortico-basal ganglia-thalamic circuit model, learns to suppress pathological alpha-beta oscillations by 45.2% while reducing stimulation charge by 80.0% relative to continuous DBS. Sparsity-constrained knowledge distillation compresses the policy onto the SynSense XyloAudio 3 neuromorphic processor at 0.52 mW inference power, yielding 28.1x lower energy per inference than an equivalent artificial neural network on conventional edge hardware. By co-optimizing stimulation energy and inference efficiency, the framework addresses both major power demands in implantable neuromodulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces energy-aware learning for adaptive deep brain stimulation (DBS) in Parkinson's disease. A deep spiking Q-network is trained via reinforcement learning inside a biophysical cortico-basal ganglia-thalamic circuit model; the reward explicitly penalizes stimulation charge. The resulting policy is reported to suppress pathological alpha-beta oscillations by 45.2% while cutting stimulation charge by 80.0% relative to continuous DBS. A sparsity-constrained knowledge-distillation step then deploys the policy on the SynSense XyloAudio 3 neuromorphic processor at 0.52 mW, achieving 28.1× lower energy per inference than an equivalent ANN on conventional edge hardware.

Significance. If the underlying biophysical model is shown to reproduce human LFP spectra and DBS responses, the work would be significant for implantable neuromodulation: it jointly optimizes actuator energy (via the RL reward) and inference energy (via spiking networks and neuromorphic deployment). The explicit inclusion of actuator cost in the learning objective and the end-to-end hardware mapping are concrete strengths that address both dominant power sinks in closed-loop DBS.

major comments (2)
  1. [Abstract] Abstract: all quantitative claims (45.2% oscillation suppression, 80.0% charge reduction, 28.1× energy reduction) are generated exclusively inside the cortico-basal ganglia-thalamic model. No cross-validation against human LFP spectra, patient-specific parameters, or alternative models is described, rendering the reported percentages clinically uninterpretable without that match.
  2. [Abstract] Abstract: the central performance numbers are presented without any description of the training procedure, choice of baselines, statistical tests, number of runs, or error bars. This absence prevents assessment of robustness and is load-bearing for the claim that the policy outperforms continuous DBS.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the abstract. We agree that the abstract should better contextualize the simulation-based nature of the results and include key methodological details for assessing robustness. We will revise the abstract and add supporting text in the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: all quantitative claims (45.2% oscillation suppression, 80.0% charge reduction, 28.1× energy reduction) are generated exclusively inside the cortico-basal ganglia-thalamic model. No cross-validation against human LFP spectra, patient-specific parameters, or alternative models is described, rendering the reported percentages clinically uninterpretable without that match.

    Authors: We acknowledge that all reported metrics are obtained within the computational model and that the abstract does not explicitly reference external validation. The cortico-basal ganglia-thalamic model employed is a standard biophysical model previously shown in the literature to reproduce human LFP spectra and DBS response characteristics; we will add citations to these validation studies in the revised abstract and expand the discussion section to clarify the model's established fidelity. Direct cross-validation on new human datasets or patient-specific tuning lies outside the scope of this in silico study, but the framework is intended to support such extensions. revision: partial

  2. Referee: [Abstract] Abstract: the central performance numbers are presented without any description of the training procedure, choice of baselines, statistical tests, number of runs, or error bars. This absence prevents assessment of robustness and is load-bearing for the claim that the policy outperforms continuous DBS.

    Authors: The abstract is constrained by length, but the full manuscript details the RL training procedure (including the spiking Q-network architecture, reward formulation, and optimization), the continuous DBS baseline, statistical comparisons, and results aggregated over multiple independent runs with error bars (see Methods and Results sections). We will revise the abstract to concisely note that performance is averaged over N independent training runs with statistical testing against the baseline. revision: yes

Circularity Check

0 steps flagged

No circularity: results are simulation outcomes, not reductions by construction

full rationale

The paper reports quantitative results (45.2% oscillation suppression, 80% charge reduction) as direct outputs of reinforcement learning training inside the cortico-basal ganglia-thalamic model using an energy-aware reward. No equations, fitted parameters renamed as predictions, or self-citation chains are shown that would make these percentages equivalent to the model inputs by definition. The framework is presented as a demonstration of co-optimization within the specified biophysical simulator; the model's fidelity to human data is an external validity assumption rather than a circularity in the derivation itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Central claim depends on the accuracy of the biophysical simulation model and the design of the multi-objective reward function; no independent evidence for either is provided in the abstract.

free parameters (1)
  • energy weighting factor in reward
    Balance between oscillation suppression and stimulation energy reduction must be chosen or tuned to achieve the reported trade-off.
axioms (1)
  • domain assumption The cortico-basal ganglia-thalamic circuit model accurately captures Parkinson's pathological oscillations and stimulation effects
    Invoked when training the network in the model to produce the reported suppression and charge reduction.

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Reference graph

Works this paper leans on

50 extracted references · 45 canonical work pages · 2 internal anchors

  1. [1]

    The Journal of Physiology , volume =

    A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve , author =. The Journal of Physiology , volume =. doi:10.1113/jphysiol.1952.sp004764 , urldate =

    work page doi:10.1113/jphysiol.1952.sp004764 1952

  2. [2]

    IEEE Transactions on Neural Networks , volume =

    Simple Model of Spiking Neurons , author =. IEEE Transactions on Neural Networks , volume =. doi:10.1109/TNN.2003.820440 , urldate =

    work page doi:10.1109/tnn.2003.820440 2003

  3. [3]

    Advances in Neural Information Processing Systems 32 , pages =

    PyTorch: An Imperative Style, High-Performance Deep Learning Library , author =. Advances in Neural Information Processing Systems 32 , pages =. 2019 , publisher =

    2019

  4. [4]

    and Ward, Max and Neftci, Emre O

    Eshraghian, Jason K. and Ward, Max and Neftci, Emre O. and Wang, Xinxin and Lenz, Gregor and Dwivedi, Girish and Bennamoun, Mohammed and Jeong, Doo Seok and Lu, Wei D. , year = 2023, month = sep, journal =. Training. doi:10.1109/JPROC.2023.3308088 , urldate =

    work page doi:10.1109/jproc.2023.3308088 2023

  5. [5]

    , year = 2020, month = jan, journal =

    Lu, Meili and Wei, Xile and Che, Yanqiu and Wang, Jiang and Loparo, Kenneth A. , year = 2020, month = jan, journal =. Application of. doi:10.1109/TNSRE.2019.2952637 , langid =

    work page doi:10.1109/tnsre.2019.2952637 2020

  6. [6]

    Deep Brain Stimulation of the Subthalamic Nucleus for the Treatment of

    Benabid, Alim Louis and Chabardes, Stephan and Mitrofanis, John and Pollak, Pierre , year = 2009, month = jan, journal =. Deep Brain Stimulation of the Subthalamic Nucleus for the Treatment of. doi:10.1016/S1474-4422(08)70291-6 , langid =

    work page doi:10.1016/s1474-4422(08)70291-6 2009

  7. [7]

    What Brain Signals Are Suitable for Feedback Control of Deep Brain Stimulation in

    Little, Simon and Brown, Peter , year = 2012, journal =. What Brain Signals Are Suitable for Feedback Control of Deep Brain Stimulation in. doi:10.1111/j.1749-6632.2012.06650.x , urldate =

    work page doi:10.1111/j.1749-6632.2012.06650.x 2012

  8. [8]

    and Aziz, Tipu Z

    Little, Simon and Pogosyan, Alex and Neal, Spencer and Zavala, Baltazar and Zrinzo, Ludvic and Hariz, Marwan and Foltynie, Thomas and Limousin, Patricia and Ashkan, Keyoumars and FitzGerald, James and Green, Alexander L. and Aziz, Tipu Z. and Brown, Peter , year = 2013, month = sep, journal =. Adaptive Deep Brain Stimulation in Advanced. doi:10.1002/ana.2...

    work page doi:10.1002/ana.23951 2013

  9. [9]

    and Heijmans, Margot and Kuijf, Mark L

    Habets, Jeroen G.V. and Heijmans, Margot and Kuijf, Mark L. and Janssen, Marcus L.F. and Temel, Yasin and Kubben, Pieter L. , year =. An Update on Adaptive Deep Brain Stimulation in. Movement Disorders , volume =. doi:10.1002/mds.115 , url =

    work page doi:10.1002/mds.115

  10. [10]

    Arlotti, Mattia and Marceglia, Sara and Foffani, Guglielmo and Volkmann, Jens and Lozano, Andres M. and Moro, Elena and Cogiamanian, Filippo and Prenassi, Marco and Bocci, Tommaso and Cortese, Francesca and Rampini, Paolo and Barbieri, Sergio and Priori, Alberto , year = 2018, month = mar, journal =. Eight-Hours Adaptive Deep Brain Stimulation in Patients...

    work page doi:10.1212/wnl.0000000000005121 2018

  11. [11]

    Pathological Synchronization in

    Hammond, Constance and Bergman, Hagai and Brown, Peter , year = 2007, month = jul, journal =. Pathological Synchronization in. doi:10.1016/j.tins.2007.05.004 , urldate =

    work page doi:10.1016/j.tins.2007.05.004 2007

  12. [12]

    Journal of NeuroEngineering and Rehabilitation , volume =

    Advances in Closed-Loop Deep Brain Stimulation Devices , author =. Journal of NeuroEngineering and Rehabilitation , volume =. doi:10.1186/s12984-017-0295-1 , urldate =

    work page doi:10.1186/s12984-017-0295-1

  13. [13]

    Thakur, Chetan Singh and Molin, Jamal Lottier and Cauwenberghs, Gert and Indiveri, Giacomo and Kumar, Kundan and Qiao, Ning and Schemmel, Johannes and Wang, Runchun and Chicca, Elisabetta and Olson Hasler, Jennifer and Seo, Jae-sun and Yu, Shimeng and Cao, Yu and. Large-. Frontiers in Neuroscience , volume =. doi:10.3389/fnins.2018.00891 , urldate =

    work page doi:10.3389/fnins.2018.00891 2018

  14. [14]

    Journal of Computational Neuroscience , volume =

    High Frequency Stimulation of the Subthalamic Nucleus Eliminates Pathological Thalamic Rhythmicity in a Computational Model , author =. Journal of Computational Neuroscience , volume =

  15. [15]

    and Grill, Warren M

    Kumaravelu, Karthik and Brocker, David T. and Grill, Warren M. , year = 2016, month = apr, journal =. A Biophysical Model of the Cortex-Basal Ganglia-Thalamus Network in the 6-. doi:10.1007/s10827-016-0593-9 , langid =

    work page doi:10.1007/s10827-016-0593-9 2016

  16. [16]

    IEEE Neural Engineering Conference (NER) , year =

    Accelerating Neuromorphic Deep Brain Stimulation Optimization through Knowledge Distillation and Enforced Sparsity , author =. IEEE Neural Engineering Conference (NER) , year =

  17. [17]

    Nguyen, Binh and Mighetto, Edward and Louie, Dylan and Yu, Chunxiu and Eshraghian, Jason , year = 2025, month = may, pages =. Closed-. 2025. doi:10.1109/ISCAS56072.2025.11043472 , urldate =

    work page doi:10.1109/iscas56072.2025.11043472 2025

  18. [18]

    Nature Communications , volume =

    Efficient Event-Based Delay Learning in Spiking Neural Networks , author =. Nature Communications , volume =. doi:10.1038/s41467-025-65394-8 , urldate =

    work page doi:10.1038/s41467-025-65394-8

  19. [19]

    Neural Computing and Applications , volume =

    Energy Efficient and Low-Latency Spiking Neural Networks on Embedded Microcontrollers through Spiking Activity Tuning , author =. Neural Computing and Applications , volume =. doi:10.1007/s00521-024-10191-5 , urldate =

    work page doi:10.1007/s00521-024-10191-5

  20. [20]

    Nature Communications , volume =

    Neuromorphic Hardware for Somatosensory Neuroprostheses , author =. Nature Communications , volume =. doi:10.1038/s41467-024-44723-3 , urldate =

    work page doi:10.1038/s41467-024-44723-3

  21. [21]

    and Gurram, Sandeep and Kamble, Nitish and Yadav, Ravi and Srinivas, Dwarakanath and Pal, Pramod K

    Sharma, Praveen and Holla, Vikram V. and Gurram, Sandeep and Kamble, Nitish and Yadav, Ravi and Srinivas, Dwarakanath and Pal, Pramod K. , year = 2023, journal =. A. doi:10.4103/aian.aian_62_23 , urldate =

    work page doi:10.4103/aian.aian_62_23 2023

  22. [22]

    and Bauer, Felix and Weidel, Philipp , title =

    Muir, Dylan R. and Bauer, Felix and Weidel, Philipp , title =. doi:10.5281/zenodo.3773845 , url =

    work page doi:10.5281/zenodo.3773845

  23. [23]

    Bos, Hannah and Muir, Dylan , year = 2022, month = sep, number =. Sub-. doi:10.48550/arXiv.2208.12991 , urldate =. arXiv , keywords =:2208.12991 , primaryclass =

    work page doi:10.48550/arxiv.2208.12991 2022

  24. [24]

    2019 , organization =

    Jetson. 2019 , organization =

    2019

  25. [25]

    Pedersen, Jens E. and Abreu, Steven and Jobst, Matthias and Lenz, Gregor and Fra, Vittorio and Bauer, Felix Christian and Muir, Dylan Richard and Zhou, Peng and Vogginger, Bernhard and Heckel, Kade and Urgese, Gianvito and Shankar, Sadasivan and Stewart, Terrence C. and Sheik, Sadique and Eshraghian, Jason K. , year = 2024, month = sep, journal =. Neuromo...

    work page doi:10.1038/s41467-024-52259-9 2024

  26. [26]

    Accelerating

    Pierro, Alessandro and Abreu, Steven and Timcheck, Jonathan and Stratmann, Philipp and Wild, Andreas and Shrestha, Sumit Bam , year = 2025, month = aug, number =. Accelerating. doi:10.48550/arXiv.2502.01330 , urldate =. arXiv , keywords =:2502.01330 , primaryclass =

    work page doi:10.48550/arxiv.2502.01330 2025

  27. [27]

    , year =

    Kuzmina, Ekaterina and Kriukov, Dmitrii and Lebedev, Mikhail and Dylov, Dmitry V. , year =. Neurophysiologically. doi:10.48550/arXiv.2505.09624 , url =. 2505.09624 , archiveprefix =

    work page doi:10.48550/arxiv.2505.09624

  28. [28]

    2004 , month = nov, journal =

    Selection of Stimulus Parameters for Deep Brain Stimulation , author =. 2004 , month = nov, journal =. doi:10.1016/j.clinph.2004.05.031 , url =

    work page doi:10.1016/j.clinph.2004.05.031 2004

  29. [29]

    2021 , month = feb, journal =

    Technology of Deep Brain Stimulation: Current Status and Future Directions , author =. 2021 , month = feb, journal =. doi:10.1038/s41582-020-00426-z , url =

    work page doi:10.1038/s41582-020-00426-z 2021

  30. [30]

    and Pajic, Miroslav , year =

    Gao, Qitong and Naumann, Michael and Jovanov, Ilija and Lesi, Vuk and Kamaravelu, Karthik and Grill, Warren M. and Pajic, Miroslav , year =. Model-. 2020. doi:10.1109/ICCPS48487.2020.00018 , url =

    work page doi:10.1109/iccps48487.2020.00018 2020

  31. [31]

    , year = 2019, month = sep, journal =

    Su, Fei and Kumaravelu, Karthik and Wang, Jiang and Grill, Warren M. , year = 2019, month = sep, journal =. Model-. doi:10.3389/fnins.2019.00956 , urldate =

    work page doi:10.3389/fnins.2019.00956 2019

  32. [32]

    Proceedings of the National Academy of Sciences , volume =

    Temporal Evolution of Beta Bursts in the Parkinsonian Cortical and Basal Ganglia Network , author =. Proceedings of the National Academy of Sciences , volume =. doi:10.1073/pnas.1819975116 , urldate =

    work page doi:10.1073/pnas.1819975116

  33. [33]

    Stanslaski, Scott and Summers, Rebekah L. S. and Tonder, Lisa and Tan, Ye and Case, Michelle and Raike, Robert S. and Morelli, Nathan and Herrington, Todd M. and Beudel, Martijn and Ostrem, Jill L. and Little, Simon and Almeida, Leonardo and. Sensing Data and Methodology from the. npj Parkinson's Disease , volume =. doi:10.1038/s41531-024-00772-5 , urldate =

    work page doi:10.1038/s41531-024-00772-5

  34. [34]

    JAMA Neurology , volume =

    Long-. JAMA Neurology , volume =. doi:10.1001/jamaneurol.2025.2781 , urldate =

    work page doi:10.1001/jamaneurol.2025.2781 2025

  35. [35]

    Long-Term Wireless Streaming of Neural Recordings for Circuit Discovery and Adaptive Stimulation in Individuals with

    Gilron, Ro'ee and Little, Simon and Perrone, Randy and Wilt, Robert and. Long-Term Wireless Streaming of Neural Recordings for Circuit Discovery and Adaptive Stimulation in Individuals with. Nature Biotechnology , volume =. doi:10.1038/s41587-021-00897-5 , urldate =

    work page doi:10.1038/s41587-021-00897-5

  36. [36]

    Li, Zongyi and Kovachki, Nikola and Azizzadenesheli, Kamyar and Liu, Burigede and Bhattacharya, Kaushik and Stuart, Andrew and Anandkumar, Anima , year = 2021, month = may, number =. Fourier. doi:10.48550/arXiv.2010.08895 , urldate =. arXiv , keywords =:2010.08895 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2010.08895 2021

  37. [37]

    DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

    Lu, Lu and Jin, Pengzhan and Karniadakis, George Em , year = 2021, month = mar, journal =. doi:10.1038/s42256-021-00302-5 , urldate =. arXiv , keywords =:1910.03193 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s42256-021-00302-5 2021

  38. [38]

    , year = 2020, journal =

    Liu, Chen and Zhao, Ge and Wang, Jiang and Wu, Hao and Li, Huiyan and Fietkiewicz, Chris and Loparo, Kenneth A. , year = 2020, journal =. Neural

    2020

  39. [39]

    Cho, Chia-Hung and Huang, Pin-Jui and Chen, Meng-Chao and Lin, Chii-Wann , year = 2024, journal =. Closed-. doi:10.1109/TNSRE.2024.3465243 , urldate =

    work page doi:10.1109/tnsre.2024.3465243 2024

  40. [40]

    , year = 2014, month = nov, journal =

    Ebert, Martin and Hauptmann, Christian and Tass, Peter A. , year = 2014, month = nov, journal =. Coordinated Reset Stimulation in a Large-Scale Model of the. doi:10.3389/fncom.2014.00154 , urldate =

    work page doi:10.3389/fncom.2014.00154 2014

  41. [41]

    Jarvis, M. R. and Mitra, P. P. , year = 2001, month = apr, journal =. Sampling. doi:10.1162/089976601300014312 , urldate =

    work page doi:10.1162/089976601300014312 2001

  42. [42]

    Annals of Neurology , volume =

    Calculating Total Electrical Energy Delivered by Deep Brain Stimulation Systems , author =. Annals of Neurology , volume =. doi:10.1002/ana.20525 , urldate =

    work page doi:10.1002/ana.20525

  43. [43]

    Cho, Kyunghyun and. On the. Proceedings of. doi:10.3115/v1/W14-4012 , urldate =

    work page doi:10.3115/v1/w14-4012

  44. [44]

    Velisar, A. and. Dual Threshold Neural Closed Loop Deep Brain Stimulation in. Brain Stimulation , volume =. doi:10.1016/j.brs.2019.02.020 , urldate =

    work page doi:10.1016/j.brs.2019.02.020 2019

  45. [45]

    Sensors (Basel, Switzerland) , volume =

    A. Sensors (Basel, Switzerland) , volume =. doi:10.3390/s22176429 , urldate =

    work page doi:10.3390/s22176429

  46. [46]

    Comparison of the

    Helmers, Ann-Kristin and L. Comparison of the. Neuromodulation: Journal of the International Neuromodulation Society , volume =. doi:10.1111/ner.12720 , langid =

    work page doi:10.1111/ner.12720

  47. [47]

    Implantable

    Sarica, Can and. Implantable. Frontiers in Human Neuroscience , volume =. doi:10.3389/fnhum.2021.708481 , urldate =

    work page doi:10.3389/fnhum.2021.708481 2021

  48. [48]

    Science Translational Medicine , volume =

    Optimized Temporal Pattern of Brain Stimulation Designed by Computational Evolution , author =. Science Translational Medicine , volume =. doi:10.1126/scitranslmed.aah3532 , langid =

    work page doi:10.1126/scitranslmed.aah3532

  49. [49]

    Neurology , volume =

    Nine-Year Prospective Efficacy and Safety of Brain-Responsive Neurostimulation for Focal Epilepsy , author =. Neurology , volume =. doi:10.1212/WNL.0000000000010154 , urldate =

    work page doi:10.1212/wnl.0000000000010154

  50. [50]

    and Deer, Timothy R

    Mekhail, Nagy and Levy, Robert M. and Deer, Timothy R. and Kapural, Leonardo and Li, Sean and Amirdelfan, Kasra and Hunter, Corey W. and Rosen, Steven M. and Costandi, Shrif J. and Falowski, Steven M. and Burgher, Abram H. and Pope, Jason E. and Gilmore, Christopher A. and Qureshi, Farooq A. and Staats, Peter S. and Scowcroft, James and Carlson, Jonathan ...

    work page doi:10.1016/s1474-4422(19)30414-4 2020