Using analog computers in today's largest computational challenges
Anabrid GmbH, Am Stadtpark 3, 12167 Berlin, Germany
Bernd Ulmann
Anabrid GmbH, Am Stadtpark 3, 12167 Berlin, Germany
Lars Heimann
Anabrid GmbH, Am Stadtpark 3, 12167 Berlin, Germany
Dirk Killat
Anabrid GmbH, Am Stadtpark 3, 12167 Berlin, Germany
Microelectronics Department, Brandenburg University of Technology, 03046 Cottbus, Germany
Related authors
Dirk Killat, Bernd Ulmann, and Sven Köppel
Adv. Radio Sci., 21, 89–100, https://doi.org/10.5194/ars-21-89-2023, https://doi.org/10.5194/ars-21-89-2023, 2023
Short summary
Short summary
Analog integrators have the problem that small signals are affected by the noise of the circuit and large signals are limited by the supply voltage. In the hybrid integrator, mixed digital and analog signal processing increases the maximum possible difference between the smallest and largest signals, which can be almost any size. The hybrid integrator has improved detection of dynamic input signals, which further improves the dynamic range.
Dirk Killat, Bernd Ulmann, and Sven Köppel
Adv. Radio Sci., 21, 89–100, https://doi.org/10.5194/ars-21-89-2023, https://doi.org/10.5194/ars-21-89-2023, 2023
Short summary
Short summary
Analog integrators have the problem that small signals are affected by the noise of the circuit and large signals are limited by the supply voltage. In the hybrid integrator, mixed digital and analog signal processing increases the maximum possible difference between the smallest and largest signals, which can be almost any size. The hybrid integrator has improved detection of dynamic input signals, which further improves the dynamic range.
Stefan Bramburger and Dirk Killat
Adv. Radio Sci., 17, 161–167, https://doi.org/10.5194/ars-17-161-2019, https://doi.org/10.5194/ars-17-161-2019, 2019
Stefan Bramburger, Benny Zinke, and Dirk Killat
Adv. Radio Sci., 15, 163–168, https://doi.org/10.5194/ars-15-163-2017, https://doi.org/10.5194/ars-15-163-2017, 2017
Short summary
Short summary
Analog environmental signals must be converted to digital for processing and transmitting. This analog to digital conversion is usually done with a constant rate. To save energy during conversion and transmission this conversion rate can be made adaptable to the signal form, which is called asynchronous A-to-D conversion. Before digital processing the asynchronous sampled data must be interpolated to a constant rate. This interpolation is subject of the article. The work was funded by the DFG.
S. Pashmineh and D. Killat
Adv. Radio Sci., 13, 109–120, https://doi.org/10.5194/ars-13-109-2015, https://doi.org/10.5194/ars-13-109-2015, 2015
Short summary
Short summary
This paper presents two high-voltage circuits used in power management, a switching driver for buck converter with optimized on-resistance and a low dropout (LDO) voltage regulator with 2-stacked pMOS pass devices. The circuit design is based on stacked MOSFETs, thus the circuits are technology independent.
Cited articles
Amant, R., Yazdanbakhsh, A., Park, J., Thwaites, B., Esmaeilzadeh, H., Hassibi,
A., Ceze, L., and Burger, D.: General-purpose code acceleration with
limited-precision analog computation, in: ACM/IEEE 41st International Symposium on Computer Architecture (ISCA), vol. 42, pp. 505–516,
https://doi.org/10.1109/ISCA.2014.6853213, 2014. a
Bishop, K. and Green, D.: Hybrid Computer Impelementation of the Alternating
Direction Implicit Procedure for the Solution of Two-Dimensional, Parabolic,
Partial-Differential Equations, AIChE Journal, 16, 139–143, https://doi.org/10.1002/aic.690160126, 1970. a
Bournez, O. and Pouly, A.: A Survey on Analog Models of Computation, in: Handbook of Computability and Complexity, Springer, Cham, pp. 173–226, https://doi.org/10.1007/978-3-030-59234-9_6, 2021. a
Breems, L., Bolatkale, M., Brekelmans, H., Bajoria, S., Niehof, J., Rutten, R.,
Oude-Essink, B., Fritschij, F., Singh, J., and Lassche, G.: A 2.2 GHz
Continuous-Time Delta Sigma ADC With −102 dBc THD and 25 MHz
Bandwidth, IEEE J. Solid-St. Circ., 51, 2906–2916,
https://doi.org/10.1109/jssc.2016.2591826, 2016. a
Brezis, H. and Browder, F.: Partial Differential Equations in the 20th Century,
Adv. Math., 135, 76–144, https://doi.org/10.1006/aima.1997.1713, 1998. a
Calude, C. S., Pa˘un, G., and Ta˘ta˘râm, M.: A Glimpse into natural computing. Centre for Discrete Mathematics and Theoretical Computer Science, The University of Auckland, New Zealand, available at: https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/download.php?selected-id=93 (last access: 2 August 2021), 1999. a
Chu, C.: Numerical Methods in Fluid Dynamics, Adv.
Appl. Mech., 18, 285–331,
https://doi.org/10.1016/S0065-2156(08)70269-2, 1979. a
Cockburn, B. and Shu, C.-W.: Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems, J. Sci. Comput., 16, 173–261,
https://doi.org/10.1023/A:1012873910884, 2001. a, b
Cowan, G., Melville, R. C., and Tsividis, Y. P.: A VLSI analog computer/math
co-processor for a digital computer, ISSCC Dig. Tech. Pap. I, San Francisco, CA, USA, 10–10 February 2005, vol. 1, pp. 82–586, https://doi.org/10.1109/ISSCC.2005.1493879,
2005. a
Cowan, G. E. R.: A VLSI analog computer/math co-processor for a digital
computer, PhD thesis, Columbia University, available at: http://www.cisl.columbia.edu/grads/gcowan/vlsianalog.pdf (last access: 2 August 2021), 2005. a
Dahlquist, G. and Jeltsch, R.: Generalized disks of contractivity for explicit and implicit
Runge-Kutta methods, Royal Institute of Technology, Stockholm, Sweden, available at: https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-20.pdf (last access: 2 August 2021), 1979. a
Deaton, R., Garzon, M., Rose, J., Franceschetti, D., and Stevens, S.: DNA
Computing: A Review, Fund. Inform., 35, 231–245,
https://doi.org/10.3233/FI-1998-35123413, 1998. a
de Melo, A. C.: The New Linux 'perf' Tools, Tech. rep., available at:
http://vger.kernel.org/~acme/perf/lk2010-perf-paper.pdf (last access: 27 July 2021),
2010. a
Diot, S., Loubère, R., and Clain, S.: The MOOD method in the
three-dimensional case: Very-High-Order Finite Volume Method for Hyperbolic
Systems, Int. J. Numer. Meth. Fl., 73, 362–392
https://doi.org/10.1002/fld.3804,
2013. a
Dumbser, M., Balsara, D. S., Toro, E. F., and Munz, C.-D.: A unified framework
for the construction of one-step finite volume and discontinuous Galerkin
schemes on unstructured meshes, J. Comput. Phys., 227,
8209–8253, https://doi.org/10.1016/j.jcp.2008.05.025, 2008. a
Fambri, F., Dumbser, M., Köppel, S., Rezzolla, L., and Zanotti, O.: ADER
discontinuous Galerkin schemes for general-relativistic ideal
magnetohydrodynamics, Mon. Not. R. Astron. Soc., 477, 4543–4564,
https://doi.org/10.1093/mnras/sty734, 2018. a
Feilmeier, M.: Hybridrechnen, Springer, Basel, https://doi.org/10.1007/978-3-0348-5490-0, 1974. a
Georgescu, I. M., Ashhab, S., and Nori, F.: Quantum simulation, Rev.
Mod. Phys., 86, 153–185, https://doi.org/10.1103/revmodphys.86.153, 2014. a
Gruber, T., Eitzinger, J., Hager, G., and Wellein, G.: LIKWID 5: Lightweight
Performance Tools, Zenodo [data set], https://doi.org/10.5281/zenodo.4275676, 2020. a
Gustafson, J. L.: Reevaluating Amdahl′s law, Commun. ACM, 31, 532–533, https://doi.org/10.1145/42411.42415, 1988. a
Hager, G., Wellein, G., and Treibig, J.: LIKWID: A Lightweight
Performance-Oriented Tool Suite for x86 Multicore Environments, in: 2010 39th
International Conference on Parallel Processing Workshops, IEEE
Computer Society, Los Alamitos, CA, USA, 13–16 September 2010, pp. 207–216, https://doi.org/10.1109/ICPPW.2010.38, 2010. a
Harten, A.: High resolution schemes for hyperbolic conservation laws, J.
Computat. Phys., 135, 260–278, https://doi.org/10.1006/jcph.1997.5713, 1997. a
Hirsch, C.: Numerical computation of internal and external flows, in: Computational Methods for Inviscid and Viscous Flows, vol.
2, John Wiley & Sons, Chichester, England and New York, 1990. a
Huang, Y., Guo, N., Seok, M., Tsividis, Y., Mandli, K., and Sethumadhavan, S.:
Hybrid analog-digital solution of nonlinear partial differential equations,
in: Proceedings of the 50th Annual IEEE/ACM International Symposium on
Microarchitecture, ACM, 665–678, https://doi.org/10.1145/3123939.3124550, 2017. a
Karplus, W. and Russell, R.: Increasing Digital Computer Efficiency with the
Aid of Error-Correcting Analog Subroutines, IEEE T. Comput.,
C-20, 831–837, https://doi.org/10.1109/T-C.1971.223357 1971. a
Kendon, V. M., Nemoto, K., and Munro, W. J.: Quantum analogue computing,
Philos. T. R. Soc. A, 368, 3609–3620, https://doi.org/10.1098/rsta.2010.0017, 2010. a
Köppel, S.: Towards an exascale code for GRMHD on dynamical spacetimes,
J. Phys. Conf. Ser., 1031, 012017,
https://doi.org/10.1088/1742-6596/1031/1/012017, 2018. a
MacLennan, B. J.: Natural computation and non-Turing models of computation,
Theor. Comput. Sci., 317, 115–145, https://doi.org/10.1016/j.tcs.2003.12.008, 2004. a
MacLennan, B. J.: Analog Computation, in: Computational Complexity, edited by: Meyers, R., Springer, New York, pp.
161–184, https://doi.org/10.1007/978-1-4614-1800-9_12, 2012. a
MacLennan, B. J.: Unconventional Computing, University of Tennessee, Knoxville, Tennessee, USA, available at:
http://web.eecs.utk.edu/~bmaclenn/Classes/494-594-UC/handouts/UC.pdf (last access: 27 July 2021),
2019. a
Michoski, C., Milosavljević, M., Oliver, T., and Hatch, D. R.: Solving
differential equations using deep neural networks, Neurocomputing, 399,
193–212, https://doi.org/10.1016/j.neucom.2020.02.015, 2020. a
Nomura, T. and Deiters, R.: Improving the analog simulation of partial
differential equations by hybrid computation, Simulation, 11, 73–80, https://doi.org/10.1177/003754976801100207, 1968. a
Reihing, J.: A time-sharing analog computer, in: Proceedings of the western
joint computer conference, San Francisco, CA, USA, 3–5 March 1959, 341–349, https://doi.org/10.1145/1457838.1457904, 1959. a
Rodgers, D. P.: Improvements in Multiprocessor System Design, SIGARCH Comput.
Archit. News, 13, 225–231, https://doi.org/10.1145/327070.327215, 1985. a, b
Röhl, T., Eitzinger, J., Hager, G., and Wellein, G.: LIKWID Monitoring Stack: A Flexible Framework Enabling Job Specific Performance monitoring for the masses, 2017 IEEE International Conference on Cluster Computing (CLUSTER), Honolulu, HI, USA, 5–8 September 2017, 781–784, https://doi.org/10.1109/CLUSTER.2017.115, 2017. a
Schenck, C. and Fox, D.: Spnets: Differentiable fluid dynamics for deep neural networks, in: Conference on Robot Learning, PMLR, 87, 317–335,
available at: http://proceedings.mlr.press/v87/schenck18a.html (last access: 27 July 2021), 2018. a
Schuman, C. D., Potok, T. E., Patton, R. M., Birdwell, J. D., Dean, M. E.,
Rose, G. S., and Plank, J. S.: A Survey of Neuromorphic Computing and Neural
Networks in Hardware, arXiv [preprint], arXiv:1705.06963v1,
19 May 2017. a
Shu, C.-W.: High order WENO and DG methods for time-dependent
convection-dominated PDEs: A brief survey of several recent developments,
J. Comput. Phys., 316, 598–613,
https://doi.org/10.1016/j.jcp.2016.04.030, 2016. a
Siegelmann, H. T.: Computation Beyond the Turing Limit, Science, 268, 545–548,
https://doi.org/10.1126/science.268.5210.545, 1995. a
Sod, G.: Numerical Methods in Fluid Dynamics: Initial and Initial
Boundary-Value Problems, Cambridge University Press, Cambridge, UK, 1985. a
Subramaniam, B., Saunders, W., Scogland, T., and Feng., W.-c.: Trends in
Energy-Efficient Computing: A Perspective from the Green500, in: Proceedings
of the International Green Computing Conference, Arlington, VA, USA, 27–29 June 2013, https://doi.org/10.1109/IGCC.2013.6604520, 2013. a
Subramaniam, B., Scogland, T., Feng, W.-c., Cameron, K. W., and Lin, H.: Green 500 List, 2020, available at: http://www.green500.org (last access: 28 July 2021),
2020. a
Titarev, V. A. and Toro, E. F.: ADER: Arbitrary High Order Godunov Approach, J. Sci. Comput., 17, 609–618,
https://doi.org/10.1023/A:1015126814947, 2002.
a
Titarev, V. A. and Toro, E. F.: ADER schemes for three-dimensional non-linear
hyperbolic systems, J. Comput. Phys., 204, 715–736,
https://doi.org/10.1016/j.jcp.2004.10.028, 2005. a
Toro, E. F.: Primitive, Conservative and Adaptive Schemes for Hyperbolic
Conservation Laws, in: Numerical Methods for Wave Propagation. Fluid Mechanics and Its Applications, edited by: Toro, E. F. and Clarke, J. F., vol. 47,
Springer, Dordrecht, the Netherlands, pp. 323–385, https://doi.org/10.1007/978-94-015-9137-9_14, 1998. a
Ulmann, B.: Analog and Hybrid Computer Programming, De Gruyter Oldenbourg, Berlin, Boston, https://doi.org/10.1515/9783110662207, 2020. a, b
Vichnevetsky, R.: A new stable computing method for the serial hybrid computer
integration of partial differential equations, in: Spring Joint Computer
Conference, Atlantic City New Jersey, 30 April–2 May 1968, 143–150, https://doi.org/10.1145/1468075.1468098, 1968. a
Vichnevetsky, R.: Hybrid methods for partial differential equations,
Simulation, 16, 169–180, 1971. a
Volynskii, B. A. and Bukham, V. Y.: Analogues for the Solution of Boundary-Value Problems, 1st edn., in:
International Tracts in Computer Science and Technology and Their Application, Oxford, London, 1965. a
Wang, W., Zhu, Y., Chan, C.-H., and Martins, R. P.: A 5.35-mW 10-MHz
Single-Opamp Third-Order CT Delta Sigma Modulator With CTC Amplifier and
Adaptive Latch DAC Driver in 65-nm CMOS, IEEE J. Solid-St.
Circ., 53, 2783–2794, https://doi.org/10.1109/jssc.2018.2852326, 2018. a
Wang, Y., Yu, B., Berto, F., Cai, W., and Bao, K.: Modern numerical methods and
theirapplications in mechanical engineering, Adv. Mech.
Eng., 11, 1–3, https://doi.org/10.1177/1687814019887255, 2019. a
Wilhelm, F., Steinwandt, R., Langenberg, B., Liebermann, P., Messinger, A.,
Schuhmacher, P., and Misra-Spieldenner, A.: Status of quantum computer development, Version 1.2, BSI Project Number 283, Federal Office for Information Security, available at: https://www.bsi.bund.de/SharedDocs/Downloads/DE/BSI/Publikationen/Studien/Quantencomputer/P283_QC_Studie-V_1_2.html (last access: 28 July 2021), 2020. a
Zhou, Y., Stoudenmire, E. M., and Waintal, X.: What Limits the Simulation of
Quantum Computers?, Phys. Rev. X, 10, 041038, https://doi.org/10.1103/physrevx.10.041038,
2020. a
Ziegler, M.: Novel hardware and concepts for unconventional computing, Sci. Rep.,
10, 11843, https://doi.org/10.1038/s41598-020-68834-1, 2020. a
Short summary
This paper discusses modern applications for high performance analog and hybrid computer. In the first part, we do a theoretical prediction concerning the properties of these machines. In the second part, we compare such a computer against a standard laptop CPU. We find that
the even a rather simple analog computer is actually on a par.
In the third part, we give an outlook how future highly integrated analog computers could be used to tackle very large computational problems.
This paper discusses modern applications for high performance analog and hybrid computer. In the...