Yehudah Marcus

Mechanical Neuromorphic Computing — replicating & extending “Supervised Learning in Physical Networks”

Google Colab · Python (NumPy, Matplotlib, Math)

The goal: Stern, Hexner, Rocks & Liu (PRX, 2021) show that a mechanical network — a web of nodes joined by tunable edges (think springs or resistors) — can learn a task on its own, with no central computer calculating gradients. Inputs are imposed at certain source nodes and a desired response is defined at target nodes; the network then trains itself with a purely local rule (“coupled learning”) by comparing its free response to a gently nudged one, letting each edge adjust its own conductance/stiffness using only information at its two ends. Iterating this drives the outputs toward the targets, so the material itself becomes the learning machine.

What I did: I first reproduced the paper’s results from scratch in a single Google Colab notebook — building the network, applying the local learning rule, and plotting the training error as it converges. I then extended the model with concrete physical manifestations: making the learning time-based — using numerical methods (numerical integration of the governing ODEs) to evolve the network in time rather than jumping straight to a steady state — and imposing physically meaningful constraints such as positive pressures / flows, so the abstract model behaves more like a real, buildable physical system — i.e. more realizable.

Reference: M. Stern, D. Hexner, J. W. Rocks & A. J. Liu, “Supervised Learning in Physical Networks: From Machine Learning to Learning Machines,” Phys. Rev. X 11, 021045 (2021).

CFD Analysis of a NASA Canard-Controlled Missile (Spalart–Allmaras)

Ansys Fluent · Compressible RANS (Spalart–Allmaras) · Course final project (team of 3 — I ran the CFD end to end)

The goal: Reproduce and validate the supersonic aerodynamics of a NASA canard-controlled missile against published wind-tunnel data, across a range of angles of attack and Mach numbers.

What I did:

• Generated the mesh with local sizing on the critical regions (nose, canards, fins), keeping high orthogonal quality and low skewness.
• Modeled compressible flow with the Spalart–Allmaras turbulence model — inlet conditions taken from the reference, solving for the outlet pressures.
• Ran a parametric sweep over angle of attack (recomputing the moment-reference centroid for each angle) and Mach number.
• Extracted all aerodynamic forces and coefficients (normal/axial, lift/drag, moments) for future validation.

References (geometry & validation data): A. B. Blair, Jr., “Wind-Tunnel Investigation at Supersonic Speeds of a Canard-Controlled Missile With Fixed and Free-Rolling Tail Fins,” NASA Technical Paper 1316 (1978); A. B. Blair, Jr., J. M. Allen & G. Hernandez, “Canard-Controlled Missile at Supersonic Mach Numbers,” NASA Technical Paper 2157 (1983).

Optimizing Physics-Informed Neural Networks for Solving PDEs

Python · Physics-Informed Neural Networks (PINNs) · Applied Machine Learning final project, Technion

The goal: Build a state-of-the-art PINN framework that solves complex PDEs accurately and efficiently without large labeled datasets — by embedding the governing equations and boundary conditions directly into the network's loss, so the solution is forced to obey the underlying physics — and then push its accuracy with targeted enhancements.

I solved three increasingly difficult problems and validated each against analytical or high-resolution numerical solutions:

• the 1-D linear advection equation (wave speed c = 80),
• the 1-D Burgers' equation (inviscid, ν = 0),
• the incompressible Navier–Stokes equations (lid-driven cavity, Re = 100).

What I added to the baseline PINN:

• Strict periodic boundary conditions, hard-coded into the network so periodicity is enforced exactly rather than only penalized.
• Fourier feature mapping (Fourier scale 1–2) to let the network capture high-frequency components of the solution.
• Random weight factorization to improve conditioning and convergence.

Method. A 4-layer network (64 units/layer, tanh) trained with the Adam optimizer at a learning rate of 0.001 plus a learning-rate scheduler, over 50,000+ iterations. Together these enhancements markedly improved convergence and accuracy on the stiff, high-frequency, and nonlinear cases — underlining how robust PINNs can be for fluid-dynamics and wave-propagation problems.

Read the paper (PDF) →
Y. N. Marcus, “Optimizing Physics-Informed Neural Networks for Solving Partial Differential Equations,” Applied Machine Learning for Scientists and Engineers, Technion — Final Project (2025).

Treadmill — SolidWorks Design & FEA

SolidWorks (Parts, Assembly, Simulation) · Static stress + frequency (modal) analysis

The goal: Design a complete, manufacturable treadmill and verify it is both safe and dynamically sound — that it carries a running user without overstress, and that its belt roller will not resonate under repeated footfalls.

What I did:

• Modeled the full treadmill assembly and every part in SolidWorks, building each part around clear design intent (robust, edit-friendly feature trees and mates).
• Ran a static stress simulation with a person's weight applied, confirming the deck and frame stay well within safe stress and deflection limits.
• Ran a frequency (modal) simulation on the belt roller — a runner's repeated impact can excite resonance if a natural frequency sits near the footfall frequency, so this has to be checked.
• Iterated the roller so its minimum eigenfrequency ≈ 321.7 Hz — far above a runner's ~2–3 Hz footfall — while cutting its mass from 6.6 kg to 5.8 kg, keeping it light yet resonance-safe.

Noninvasive Ear-Infection Detector — VOC Sensing (Biodesign)

Technion Biomedical Engineering — Biodesign Program · Degree final project · with 2 physicians, a nurse & a product manager

The goal. Diagnosing ear infections in children today is largely subjective, which drives unnecessary antibiotic use. The aim was a noninvasive, objective, point-of-care device that gives a quick answer — not just whether a child has an ear infection, but which type (bacterial, viral, or none) — by sensing the volatile organic compounds (VOCs) that are the metabolic byproducts of each.

What I did.

• Ran the full Biodesign process — identifying and validating the clinical need, then designing a device concept to meet it — as my degree's final project in the biomedical-engineering faculty.
• Built the concept from detection methods already proven in other (sometimes unrelated) fields, making it a deliberately multidisciplinary design.
• Shaped the device around a familiar otoscope-like form factor to lower the barrier to clinical adoption.
• Iterated the design many times; built the general CAD by importing/replicating real off-the-shelf market parts and laying out the electronics separately to confirm everything packages and fits.
• Worked closely with a clinical team — two physicians, a nurse, and a product manager, all experienced in the field.

Note: the specific sensing approach is under NDA — the animation above shows the general design only.