at 11 minutes I realised this was a research paper in an easily digestable and widely available format, great work.

As a mechanical engineer who is learning computer science and machine learning, this is an amazing bridge between the two worlds! I cant wait to print some and play with the concept myself. The applications are truly endless, I wonder how long until this is made microscopically, and applied everywhere.

This is an incredible combination of an entertaining youtube video and a technical paper presentation! I wish more articles were presented like this

My heart goes out to the graduate students who did all this work. You guys are ferocious, you deserve only the best in life.

I went from complete "what is this I don't even" to "okay this makes sense, cool" in 20 minutes. Very well presented, super interesting and understandable even to someone with zero experience in mechanical engineering.

In a general sense this is what bone and connective tissues do. They have built-in stress sensors that look for electrical signals that appear in weak spots in the bone and connective tissue. They rebuild the structure to fix those weak spot s and redistribute load.

This is insane. Soon we'll be doing this kind of stuff with photolithography. Perhaps it'll be the next step in neural networks as a whole to increase efficiency.

I wonder if you could use plant cells to do something like this. Have a gas-filled vacuole inflate/deflate across a uniform foam of cells, which alters the tension against the cell walls, allowing for control over the material stiffness. plants already do this naturally to grow twards light, but imagine it being used as an organic wing. I imagine it would be made up of something like cactus flesh, filled with a microfluidic network to control local stiffness.

This is amazing. Miniaturized / nanoscale applications of this really could drive world-changing metamaterial developments. It's also a very helpful way to unpack and visualize the fairly opaque world of learning neural networks in general. I never mind waiting for content like this. Thanks so much for the walkthrough!

Very interesting! Though it feels like there will be a lot of problems with miniaturising this type of system. My intuition tells me that most miniature things wouldn't be tunable by the connections between nodes, but rather the nodes themselves. For example I could imagine a theoretical case where each node has some sort of "pressure" that it applies universilly to all of its neighbors. It may even be as simple as laying out a latice of beads either of different materials, or hollow with different air pressures or wall thicknesses. Thus, what I would be most interested in seeing next is simulating a node-pressure centric model, to see if changing the adjustable factors from the beams to them would still be able to produce the behaviours that were exhibited in this video.

I guess after trying the dynamic learning you could (mass) produce a hard-coded version with the same values and just 3D printing :)

This is fantastic way to present your paper. Very interesting research, I am looking forward to more work from your lab!

Materials Science and Engineering dropout here. I couldn’t hack it in academia at that level, I had the smarts but it was too much stress and pressure. But I still love the subject matter, I think it’s absolutely fascinating, and stuff like this video is what sent me into that field in the first place. Thank you for the detailed breakdown, this was awesome to watch.

I thought the whole point was it's a neural net where the weights have a physical meaning (i.e. the displacement), but you don't represent it that way or use gradient descent to optimize the weights. The main benefit of neural networks is that they are differentiable and so can be efficiently trained with gradient descent.

You should be able to manufacture a much cheaper and easier to scale version of this by using electro-osmotic cells (cellulose membrane tube with internal electrode between two plates is probably the simplest) as the stiffness altering actuator. Simply increase the voltage on the cell to increase the internal pressure.

Absolutely fantastic! I look forward to seeing this get progressively miniaturised.

This is an idea that I had I wanted to share with yall. This idea has been partially implemented in the video but I want to extend it. What if instead of optimizing the model in the real world you created a computer simulation that would give you more accurate results and a much faster interface (because it's software software instead of software real world). Now that you are doing the simulation part purely digitally you don't really need such a complicated mechanism to vary the stiffness. Instead, you could export the result of the computer simulation in a format readable by 3D printers. Instead of your current mechanism, you could have something like a coil that could be stiffness-manipulated by varying its width. Now, yes, this is a much less "dynamic" approach because it does not allow you to change the values on-the-fly and requires you to 3D print your material every time you want to test it in the real world but as long as your Simulation -> Real World process is accurate enough you should not need to 3D print your material every time you want to test it and should be able to do it using only software and only need to 3D print it when you want to be absolutely sure that the material behaves as it should.

I feel like having a lattice of adjustable stiffness beams is the much, much more impressive feat than the neural network part. Like, does such a lattice exist in usable ways (ie building or clothing scale devices)?

Very thought-provoking. Jolly good work from this team.

this is one of those things that is first off awesome to share with the world in this format (no way in hell i would have ever read the paper) and also an extremely interesting idea with genuine potential to change the world, thank you so much for taking the time to make such an entertaining and informative video!

Whoever made this video if I had One billion dollars I would share it with you and develop this with you. Excellent explanation, rare I find something of such high quality.

...mind totally blown! Mechanical neural networks, and you just demonstrated it! In my face! Oh goddess that's so beautiful, tyvm...x

Thanks for this, this is super cool! It's given me inspiration for a potential project of my own, albeit much lower budget and tech. Consider a PLA 3D printed lattice in a similar configuration as the triangular one you used here, but using a slight curve on the beams to allow them to bend. Consider then pressing the lattice into a mold with a force, to the point of plastic deformation. The plastic deformation of the compliant mechanisms - the damage the beams suffer - could serve as a kind of learning process, reducing the weights of certain beams, and increasing the strain and thus weights on others. Setting this apart from traditional machine learning - aside from the medium - is that the training is not easily reversible; the plastic deformation can't be undone, and for a weakened beam to become relevant again can only happen within the context of other interacting beams becoming relatively weaker too. Thus, I don't think it could learn many behaviours, as the system is essentially lossy. I'm not aware of any literature that tests neural networks whose weights can only ever shift in one direction; they would naturally be less accurate, and you would have to take a very slow and conservative learning approach so as not to totally collapse the system, but I would be very interested to see how it goes. Perhaps I'll start off with that kind of computational model. I'm also not sure how effectively it would work with simply molding it to shape, as it could use the mold as a crutch with different output forces on different locations, resulting in a different shape when not constrained by the mold. Perhaps rather than a primitive mold, then, a rig of fource gauges at the output locations could be there and seek to find where the output force is zero at the desired location; if the material is overpressuring a certain output location, you can apply a counteractive force at JUST that output location to create plastic deformation until said output force IS zero. This would have to be done conservatively and stepwise, as reducing the error at that location will inevitably create more error across the other locations; the maximal error output would have to be tweaked slightly, then the next, etc. Would love to know your thoughts, and thanks again! :)

The joys of turbulence and material science continue. It is interesting to contemplate where and how nature employs similar functions in organism behaviors.

This idea worth a Nobel prize! Great job, guys! In the future we will create a metamaterial that can morph into anything and be controlled by brain. This is real deal, I must say as an engineer.

That's a fascinating idea! Instead of deploying the learning mechanics directly, we could potentially use computer simulation and optimization to design our desired model. By simulating and optimizing the design, we can determine the best configuration without the need for a trainable machine. Once we have the optimized model, we can then build it physically, thereby bypassing the energy-intensive process of training a machine from scratch. This approach has the potential to save a tremendous amount of energy while still achieving the desired final state.

This is incredible. Bravo. So much to learn from this!

The most detailed video I have ever seen. I have only understand 1% but it is so beautiful to watch because it’s so well explained.

Such incredible stuff. I love it when work in one field is applied to another seemingly unrelated field. Just goes to show that everything in life is interconnected

This was the most mind blowing thing I've learned in the past few years! Thankyou.

This is an amazing idea. Thank you for synthesizing the concept from something that existed in software to something in the mechanical world. As this technology gets developed and shrinks in size, its applications will be limitless. This is so cool!

I´d loved to learn more about the interface of neuronal networks and machines! It was a really cool progect!

As others have already mentioned, the weights/stiffness could probably be simulated and trained on a computer so that it would be cheaper and faster. Then, once training has finished, the resulting model could be manufactured with the determined stiffness between the nodes. Regardless, this is a really great paper and video. Good job on getting featured on the front cover as well.

This is valuable! To all those people who would build on(a.k.a copying) this information, its my humble request that you please acknowledge this guy. Acknowledgement is like speaking the truth, its absence equivalent to thievery. As an EE, who absolutely depends on physics and engineering to learn a lot of math, I am thrilled to watch this. 🙏IND

This is beautiful! So many different concepts from different engineering classes are demonstrated in this video with elegant visual effects. Something especially promising seems to me to be vibration dampening. I recall that the LIGO has active vibration dampening to isolate its sensitive sensors from Earthly disturbances. If this could be trained to negate lots of different frequencies at every temperature, it would probably save some engineers somewhere a lot of work.

This format needs to be the standard for research papers going forward

Interestingly I was thinking about a mechanical neural network made up of nodes and springs with variable tensions and now I see this!! Fascinating!

This is glorious. Not least of all because I thought of it forty years ago - but I shouldn't say that. The presentation is first rate and the narrator is very easy to listen to. To see a working model of this concept is truly beautiful.

We need more research papers presented in more accessible formats like this. Great work.

Thank you for making this video Professor Hopkins!

Now to replace the magnets with ceramics for piezzo-ceramic effect to minimize the size, use the piezzo effect for both actuating and measuring the position, make it microscopic and new era of materials is here. Amazing video, great explanation and excellent visualizations. Thank you!

I really commend the accessibility and transparency of this content. Excellent work, this seems like very promising technology!

definitely helped me understand neural networks more even if not intended, Bravo!

Wow! The idea of making a material that can change its configuration based on learned input is amazing!

This is really interesting and impressive! Your video also brought some methods to my attention that may be useful to me when making topology optimization add-ons for FEM packages where only the output and not the underlying stiffness matrix is available.

I'm a Comp Sci grad and this is the first time in 20 years I've seen computer theory being applied physically. Usually, comp sci concepts are developed in the reverse direction. Incredible stuff. Very fucking cool. Congratulations to all involved.

This is a great video. I am going to watch it a few times to try and get my mind around it to some degree. I appreciate how this seems to be insight into both mechanical and AI learning. Adaptive physical algorithms designed to result in a specific task or outcome from specific inputs. The four fundamental interactions of physics are the strong and weak nuclear force, electromagnetism, and gravity. To copy a relative ranking of these relative forces: Gravitational Force - Weakest force; but has infinite range. ( Not part of the standard model) Weak Nuclear Force - Next weakest; but short range. Electromagnetic Force - Stronger, with infinite range. Strong Nuclear Force - Strongest; but short range. The four fundamental interaction of physics are interactions, these can influence on another. Consider a molecule or compound that might be adapted similar to a learning material through an influence, such as for example, electromagnetic wave interference. Can electromagnetic wave interference deliver energy or influence at an atomic or sub atomic level? Can we facilitate chemical reaction with electromagnetic wave interference? This is major question. Would it be possible to manipulate an adaptive material with wave interference? Can wave interference serve the same function as the weights or tunable beams in the artificial or mechanical neural networks? A specific application that came to mind is actually re-magnetization. If we have a field geometry that breaks down over time due to atomic re-alignment, might it be possible to efficiently and perhaps continuously re-magnetize, re-align in the desired alignment, a magnetic material, using wave interference? That is a marginal hypothetical question. We may now use electromagnetism to re-align and re-magnetize demagnetized material, however, this is a brut force approach. Might it be possible to use a more subtle, specifically targeted and efficient re-alignment, using wave interference interacting with atoms? To continue the example, if we have a microwave antenna, the physical configuration of this antenna, I believe, can create a polarized field utilizing the microwave energy. This polarized field would be within an area. Might it be possible to create a similar geometry of polarization on more of an atomic or sub atomic scale through wave interference? Perhaps an approach similar to triangulation, which might result in a specific frequency and energy at a specific point, that is also aligned in a specific manner, comparable to polarization and re-magnetization? Re-magnetization might seem a peripheral utility of adaptive materials. If we have materials that can be adapted with electromagnetism, or adapt to electromagnetism, it might have a much broader utility. The artificial or mechanical neural networks look very reminiscent of atomic or molecular structures.

There are people that legitimately think that going to space is so crazy that we havent done it. Meanwhile, were doing this. Its nuts

Excellent work and presentation! I felt hooked all the way through. I guess these lattices will at some point be etched or 3d-printed so the stiffnesses will be "hardcoded" into the geometry of the lattice elements. Basically a compliant structure with set stiffnesses. Maybe at some point the "resolution" of the lattice will become high enough so you could talk about a continuous stiffness distribution with an analytic description rather than a matrix of distinct values. Maybe behaviours could be trained in order of importance, first learning a common movement and then refining that by overlaying more precise modes of movement. Or maybe I have it backwards. On the topic of stiffness distribution, it could be represented by a bitmap. The layered compression technique in JPG format would likely go hand in hand with my previous point of layered precision.

This is fascinating research with amazing use cases via further development.

It might seem hard to compute, but in reality many neural networks are fully connected, meaning every node connects to every node in the next layer, while here each node only connects to 3 nodes in the next layer.

You could use the simulated network to generate a stiffness map for a certain behavior and then wire EDM a big aluminium plate compliant mechanism with these stiffness values. This results in a preprogrammed mechanical network that is easier to manufacture and scaleable.

Is there a reason why something like gradient descent / backpropagation wasn't used to calculate the values as opposed to evolutionary search? Was the issue that the 'hard stops' prevented backpropagation from being used?

I was a little surprised that what seemed to be a natural next step wasn't mentioned. I thought that they would construct a simple network of beams with the resultant fixed stiffneses to demonstrate that the target behaviors would be achieved.

that has to be one of the most amazing things I've seen in a while

This is a very well made documentary! Felt like I'm watching a discovery channel or reading a publication.

Incredible! So cool. I'd love to see static models developed this way

Amazing work, looking forward to seeing the progress on this and if it can be made using other methods.

This is absolutely amazing! And you just give us the designs for free. Thankyou for doing such great works!

Great. 90% research for defense industry. 🙌🙌

This is fantastic way to present your paper.

Very interesting ! Thanks !! This reminds me a conference on AI 30 years ago, explaining that very first NN consisted in fully connected arrays of transistors. Due to practical resaons (i.e. the factorial growth of soldering/wiring operations) , these arrays were limited to a very small set of elements. But their performances were promising enough to enable further works...

Have you tried incorporating static friction or backlash into the computational model? (I imagine practical applications would not exclusively use flexures and voice coils.) Have you tried 3D networks? Have you tried asymmetrical stiffness functions like Rectified Linear Unit?

I love your work and the way in which you share it with the World. Thank you for your effort and please keep doing this.

Just incredible. Thank you.

Amazing . This is what i was imaginging . Like the mechanical integrator

Amazing work and channel I'm glad to find ! A few months ago came to me this idea of mechanical computing kind of the same way you do here but with much more clumsy mechanics because I'm not engineer lol I couldn't figure out it was a neural network problem and was thinking more about a kind of crappy manual qbit processor if it makes sense to you. So I got the idea while looking at scissor extension arm and imaging that if all hinges could slide along both scissors it links, it will vary the position of the end of arm, the X,Y outputs, the start of each links of scissors being the inputs. I have the intuition that if the hinges, or node, could be controlled by some arduino and servos to slide onto the pair the result can be interesting and maybe able to achieve some of the computing you're doing here. But I now see flaws in my design that the scissor is rigid to a line and a lenght so the node hasn't as much freedom of movement as in this clever design. Insights needed for improvements and if someone wants to realise a prototype of my design please feel free but tell me :) Subscribed !

In all aspects: Great work. From the design, to the scientific exploration, to the visual presentation - excellent!

A simpler integration of this is using piezoelectric materials with electrodes placed at either end to conduct energy, where a simple change in both voltage and current direction can fluctuate the volume of the crystal. Using a material with a high piezoelectric coefficient, like PMN-PT, would generate the highest volume change and possibly be more accurate in this neural network configuration. Possibly coating fixed conducting cells with this material could allow for nano sized mechanical networks, but idk.

This almost feels like it should win some kind of award.

i remember the feeling of seeing pictures of the earliest computers, with their large, clunky electromagnets for bits, slow clock speeds, and room sized casings and thinking "look how far we've come". i hope in 60 years, i'll walk back into this video and think the same.

Wow, this is a wondrous example of engineering.

This made me think of the experiment where a programmable array was used to "evolve" a basic radio. In the end they bended up with a functional 2 way radio, but it contained components that weren't connected to any part of the circuit but could not be removed because the radio would stop working. It showed that "real world devices" might get results simulations would miss because we never thought of adding them in. I might have fuzzed up some of the details, it was some time ago I came across it.

I wonder if you can change the learning objective a bit, not asking it to learn a fixed number of random outputs, but instead, to explore the space of all input output combinations, and predict which inputs, together with which weights, correspond to which outputs. For this you could employ what's called a Quality-Diversity algorithm such as MAP-Elites. That way, once sufficiently trained, it ought to be able to more or less directly give you a pretty good guess at a configuration for some combination of inputs and outputs, likely including unseen behaviors. You could also make it more robust by randomly "damaging" some connections (leaving them at zero or maximum stiffness no matter what), meaning the network needs to find other ways to figure out what to do. And the other thing I wonder about is: just how small could you get this to be? Would it be possible to do this at microscopic scales? Each individual piece probably wouldn't have a very large range of stiffnesses, but across many layers that ought to be able to add up, giving you an extremely flexible material. Third, perhaps obviously, what about 3D? I guess you'd need a network of tetrahedra in that case for the best outcomes.

Bravo - brilliant work, groundbreaking resulting implications - truly magnificent, you guys. A spectacular achievement for the world, and for material design. Presentation and video? Satisfyingly awesome.

21:55 recalculate this but keep the number of beams constant amongst the lattices instead of the number of layers if you wish to make inferences on the orthogonal direction limitations influencing adaptability Also, in this study it's definitely the number of beams influencing time and monetary costs, not layers (which indirectly influences number of beams based on beam-to-node ratios), so it'd probably be helpful to do this test more fairly for practical reasons, too

As a mechanical engineering and computer science double major with a minor in robotics and concentration in AI this is incredibly cool. Absolutely fascinating application of AI. I’m going to fall down this rabbit hole now.

Super interesting video! Thank you a lot for sharing!

Were other lattice configurations considered or tested at any point? I'd be curious how something like a hexagonal lattice performs.

Incredible video and research. Truely next level work

Interesting. Though as a software guy this still looks to me like a simple, old-fashioned neural network, nothing mechanical about it. You have inputs (input and output forces) and outputs (the individual stiffness configurations for each beam) and try to optimize them to a certain goal. The learning still takes place on that virtual, digital layer, not on the mechanical layer. Therefore, I wouldn't have called it a "mechanical neural network", but maybe rather something like "application of neural networks to mechanical problems" - though the former is certainly snappier. Nevertheless, it is an interesting application of neural networks that is presented very well and I definitely enjoyed watching this. Please make another video once you build a bigger one!

Powerful💪😎 video amazing brother🌹🌹🌹

It is a general principle in machine learning that input nodes are exponentially more than the output nodes. This will be a much more accurate representation of a neural network. It will also be very interesting if you can recreate a feedback loop node,

Hello Jonathon! I've been following your work for quite a long time, nice to find you showing some interesting things here on YT... it's so surprising to see how few mechanism designers know about, let alone use, flexural mechanisms.... Sigh.... Great to "see" you!

Congrats on the front cover of Science!

I would love to see a physical demonstration, a built structure based on the optimized axial stiffness within chosen reason. Would be very cool to see how that preforms in practice. As for applications, not all targets will be in a triangular configuration but that is okay. As long as the target configuration can be modeled and with enough variable "nodes" as presented (which has the capacity to be optimized and exhibit desired behavior). The real trouble I imagine is tolerance in practice. This is incredible research regardless utilizing so many fields of sciences.

Well done all. Thoroughly enjoyable.

Wow, what an awesome idea! Cool topic and nice presentation! Now I think what would make this even more practical, is if you could pre-train the model, and then mass produce it with mechanical analogs to the voice coils. It would also allow the model to be scaled up or down, perhaps even to the nano scale. I notice this video on my side bar, "Tunable Stiffness Compliant Mechanism with Bistable Switch." Hmm, that looks promising. :P

Interesting demonstration. Though I'd say the material itself isn't learning anything, just being tuned by a computer. Maybe I'm just nitpicking though. Either way, this is fascinating.

Congratulations! As said by others, indeed this is a great bridge between structures and AI. Impressive!

It would be amazing to use a lattice of nitinol to do this. If you had a system to heat and cool sections of the lattice to impart memory you could really generate a lot of final outcomes. Aircraft and spacecraft/landers/rovers will be changed so much be this technology.

Correct me if I am wrong: but the stiffness is determined by the coil and the magnet, which in turn are controlled by the esp32 and the mosfets. At this stage it is the software that 'learns', not the material itself. It is not shown how the mechanical structures themselves have "learned' to behave in the same way without coils and magnets. This means that the software is a - quite complex - PID (Proportional, Integral, Derivative) routine written in code. There, all inputs (electrical, not mechanical) are read by the microprocessors, which results in the desired output being calculated and corrected after each cycle based on the comparison between the current and previous input. The power of learning is in the code: the stronger the code, the faster (fewer cycles) the desired result is achieved. Corrections - no matter how small - will always be necessary. So, in my opinion, this shows how a neural network works, but it is not mechanical. Mechanics is used to show how the learning process works. You can do that with any spring-like material. So until proven otherwise, and in the absence of any electronics, it is not a mechanical neural network. (The tuning fork shows exactly that: the fork does not learn (has not learned, will not learn) because it would change over time, which it never does)

Both brakets can be printed on the body, you can load manually to fit the coil magnet and you reduce the assembly error tolerance, number of parts and can be made smaller much easier

This is an amazing video, you made it extremely understandable and it was still very entertaining.

This could be very interesting to the construction business. Imagine the steel frame of buildings beeing designed in such a manner, that the building has a specific desireed reaction to certain stresses. It's mind blowing!

Very interesting, it proves that we have already figured out the underliying mechanism of many biological processes, great and clever work. A small caveat, I'd suggest you fully drop the inches (@19:53) from your work to avoid future confussion.

I've been bamboozled. I thought this was a fully mechanical learning mechanism but it's actually a hybrid between electronics and physical mechanisms. What I'm saying is that the neural network exists on a computer and the physical mechanism is providing feedback. Meaning that the computer doesn't have to simulate the physics in order to train the digital neural network accordingly. I read the title and thought that the physical mechanism was the network doing the training. No, it's a mechanical network of joints that is controlled by an artificial neural network.

Photon-sensitive materials which expand or contract according to LED lights can also be made. Really fascinating topic. Thank you

Microscopic material technology = huge leap forward

Dude… mind blown!! So I understand about 90% of this presentation. Jesus I would LOVE to be part of this dev.