Machine learning redesigns microscopic web sensors to be five times more flexible than nature-inspired versions, enabling detection of masses as small as trillionths of a gram.
(Nanowerk Spotlight) Mechanical sensors built at microscopic scales face a fundamental problem: they are too stiff. As structures shrink to dimensions measured in millionths of a meter, their resistance to bending increases relative to the forces they need to detect. This limits their usefulness precisely in applications like weighing individual biological particles, measuring forces exerted by cells, or detecting vibrations too faint for larger instruments.
The challenge is not merely fabrication. Even when engineers successfully build intricate microstructures, designing geometries that maximize flexibility while maintaining structural integrity requires navigating a vast space of possibilities. A web-like sensor might have a dozen or more parameters governing its shape. Each can assume thousands of values. The combinations are too numerous to search exhaustively, and the relationship between geometry and mechanical response is too complex for intuition to guide.
Researchers have looked to spiderwebs for inspiration. These natural structures combine radial spokes with spiral threads to detect tiny vibrations while withstanding environmental stresses. But translating spiderweb geometry to the microscale has not solved the stiffness problem. The radial elements that give natural webs their stability also restrict how much they can deform, limiting the flexibility of artificial versions.
A team at Beijing Institute of Technology took a different approach: rather than copying biological designs, they used machine learning to optimize beyond them. Their results, published in Advanced Materials (“Machine Learning‐Assisted Ultraelastic and Vibration‐Resolvable Microwebs”), describe suspended gold microstructures called “ultrawebs” that achieve flexibility roughly five times greater than conventional spiderweb-inspired designs when measured experimentally. Spanning just 20 µm, these devices detect mass changes at the picogram scale with sensitivity matching sensors five times their size.
Conceptual design of ultra-elastic web structures (ultraweb). (a) Schematic of a natural spider web. (b, c) Original spider web-inspired structure with limited elasticity and the generated ultraweb configuration with ultra-high elasticity by machine learning, respectively. The white arcs denote the etched lines, while the orange areas consist of Au. (d, e) Optimization process of the ultraweb through the combination of the genetic algorithm and deep learning. (Image: Reproduced with permission from Wiley-VCH Verlag) (click on image to enlarge)
The starting structure featured a central disk surrounded by nine concentric rings. The central disk serves multiple functions: it stabilizes the structure during vibration, provides a flat contact area for mechanical testing, and acts as a platform for depositing test masses.
Seventeen geometric parameters defined each design: rotation angles between successive rings and the radius of each. Encoded as 136-bit binary strings, these parameters created an enormous landscape of configurations.
Think of the central disk as a trampoline mat and the surrounding rings as its springs. The machine learning algorithm redesigned these springs to be far more responsive to tiny weights landing on the platform.
A genetic algorithm explored this space. This optimization method maintains a population of candidate solutions, evaluates their performance against a defined objective, then generates new candidates by combining traits from top performers and introducing random variations. The process mimics natural selection, progressively evolving the population toward better solutions.
Beginning with 200 random designs, the algorithm evaluated each one’s stiffness, selected the best, recombined their characteristics, introduced mutations, and repeated. Over 40 generations, the population evolved toward more flexible structures.
Direct evaluation posed a bottleneck. Computing how each candidate deforms under load requires finite-element simulation, a computational technique that divides a structure into thousands of small elements and calculates how each responds to applied forces. Each simulation takes considerable time.
The team trained a neural network on 3,500 simulations to predict mechanical behavior from geometry alone. Once trained, the network evaluated new designs almost instantaneously, allowing the algorithm to explore far more configurations than direct simulation would permit.
After 40 generations, the algorithm produced a structure visually distinct from its biological inspiration. Simulated stiffness reached approximately 0.188 nN/nm, meaning that displacing the structure by one nanometer requires less than 0.2 nanonewtons of force. The original spiderweb-mimicking design showed simulated stiffness around eight times higher.
Fabrication required extreme precision. Gold films 120 nm thick were deposited onto silicon dioxide substrates. Electron-beam lithography patterned the geometries with resolution below 10 nm. Ion-beam etching cut through the gold. Hydrofluoric acid dissolved the underlying oxide, leaving webs suspended above the substrate. Notably, exposing a 5 × 5 array of ultrawebs takes only about 15 seconds, suggesting the approach scales well for manufacturing larger sensor arrays.
Drying posed a threat to the delicate structures. Evaporating liquids exert surface tension forces that can collapse features this small. The researchers used carbon dioxide critical-point drying, which converts liquid to a supercritical state lacking surface tension before venting as gas. The webs survived intact.
Atomic force microscopy confirmed the optimization succeeded. Measured stiffness was 1.236 nN/nm for the optimized ultraweb versus 6.416 nN/nm for the original design, a fivefold improvement. The measured values exceeded simulations because a thin chromium adhesion layer added during fabrication to bond gold to the substrate increased overall rigidity. Compared to other microscale elastic structures reported in the literature, the ultrawebs achieve flexibility levels previously demonstrated only in devices spanning hundreds of micrometers.
The structures showed excellent durability. They survived 1,000 compression cycles at 150 nm displacement with fluctuations below 4.28%. Extended testing subjected them to 20 hours of continuous vibration, accumulating 10¹⁰ cycles, without damage.
Reduced stiffness improved vibration response. Driven by alternating electrical fields, optimized ultrawebs resonated at 420 kHz versus 876 kHz for original designs. Lower resonant frequencies indicate greater responsiveness to small mechanical perturbations.
For mass sensing, platinum blocks of known mass were deposited onto ultraweb centers using a focused ion beam system, allowing precise control of the added mass. As mass increased from 26.53 to 132.65 pg, resonant frequency dropped linearly at −0.801 kHz/pg. This matches sensors previously reported at five times the size, demonstrating that the optimization achieved equivalent performance in a far smaller package.
A second demonstration created mechanical encryption. Arrays mixing optimized and conventional structures encoded letters and numbers. Applying voltage at 420 kHz caused only optimized elements to vibrate detectably. A laser Doppler vibrometer scanning the array revealed the encoded pattern. Switching to 615 kHz activated intermediate-stiffness structures, displaying different content. The information remains invisible to optical microscopy and undetectable without the correct stimulus frequency.
More complex encoding used three structure types forming different patterns. Regions containing the numeral “6” and one Chinese character used the most flexible structures. Regions forming “9” and another character used intermediate designs. Background areas held the stiffest elements. Toggling stimulus frequencies switched which pattern appeared, creating encryption requiring the correct frequency key to decode.
Standard semiconductor processes enable ultraweb fabrication, suggesting integration with electronic circuits is practical. The combination of extreme mechanical responsiveness, demonstrated durability, and manufacturing compatibility positions these devices for applications in precision mass detection, vibration monitoring, and secure information systems.
The methodology extends beyond this specific application. Treating biological inspiration as a starting point for algorithmic optimization opens design possibilities that evolution never explored. Pairing genetic algorithms with neural-network acceleration applies to any problem involving complex geometries and nonlinear mechanical behavior. This work establishes that machine learning can systematically discover mechanical structures that surpass nature’s designs when optimized for specific engineering objectives.
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