William Gilpin
@wgilpin0
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asst prof @UTAustin physics @OdenInstitute interested in chaos, fluids, & biophysics.
Austin, TX
Joined May 2016
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Is chaos an analogue sampling scheme? I wrote a Perspective for
@NatRevPhys
discussing connections between classical work on information flow in nonlinear systems, and modern generative ML models
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Can machine learning predict chaos? My new paper performs a large-scale comparison of modern forecasting methods on a giant dataset of 135 chaotic systems. (1/N)
@TexasScience
@OdenInstitute
@UTPhysics
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Is chaos actually hard to predict? For NeurIPS this year I made a database of 131 known strange attractors, and trained state-of-the-art forecasting models on each one, to try to figure this out (1/N):
Paper:
Dataset + Code:
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Excited to develop a new grad computational physics course at
@TexasScience
. The entire class is open-source, incl discussions, lectures, hw, & solutions. Anyone, anywhere can access materials, and even submit pull requests/issues for bugs, typos, etc
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My new preprint explores using neural networks to learn “strange attractors” from time series. If we measure a complex system over time, can we infer additional measurement dimensions & discover underlying structure? (1/N)
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I’ll be joining the
@UTAustin
physics faculty in Fall 2022, affiliated with
@OdenInstitute
! We’ll be working on computational & experimental chaos, fluids, and data-driven modeling. I’ll be looking for students, postdocs, & visitors soon. Thanks to all who made this possible!
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The final projects for my graduate computational physics course were really cool. A group of amazing undergrads implemented Anderson localization under the tight binding model on arbitrary graphs (1/4)
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The second year of my fully open-source graduate computational physics course is now underway
@TexasScience
@OdenInstitute
We invite students anywhere in the world to participate. Mods/Issues/PRs on GitHub welcome!
(vid: condensate forms in turbulence)
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I found that large domain-agnostic models (Transformers, LSTM, etc) can forecast chaos really far into the future (>10 Lyapunov times). With enough training history, they outperform physics methods (next-gen reservoir computers, neural ODE, etc).
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I’m looking for grad students for several openings starting Fall 2022 or later! Excited to talk to students w/ diverse backgrounds interested in any combo of complex systems, machine learning, nonlinear & fluid dynamics, especially applied to biological questions (1/4)
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My new paper shows oscillators that try to synchronize, but can’t b/c of mutual repulsion and jamming. In intermediate regimes, synchronization and neighbor interactions compete to produce avalanches
@PhysRevResearch
Paper:
Code:
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I’m hiring a postdoc at UT Austin physics. We work on computational nonlinear dynamics for fluids and biological systems. We have projects with various combos of pencil-and-paper theory, coding-heavy ML for time series, and even a few tabletop experiments (1/3)
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btw here is a link to all of the code, and the full chaotic systems dataset:
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I am very grateful and excited to be on the Forbes 30 under 30 list this year! I've been very lucky to have amazing mentors like Manu supporting my career
Latest Forbes 30 under 30 list is out - fantastic to see so many upcoming young scientists work highlighted. Also proud moment to see
@wgilpin0
amongst them who is about to open doors for his brand new lab at UT Austin soon.
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It is wonderful to visit somewhere with dark skies. Here is the center of the galaxy rising over Kauai (30 second exposure)
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That model scale + large amounts of data outperform domain-specific inductive biases is known as the “bitter lesson”, and it’s a theme of recent ML works
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I’m looking for a postdoc with broad interests in any intersection of nonlinear dynamics, statistical learning, and soft matter physics. Lots of independence to pursue anything you find exciting!
Postdoc positions in soft matter, machine learning, and dynamical systems at UT Austin with
@wgilpin0
The University of Texas at Austin, USA
#ScienceJobs
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The goal of this project is to create a general-purpose tool for exploratory analysis of time series—you never know what you might find! The code is all available , and I would be excited to chat more with anyone who wants to try it out! (N/N)
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My paper on learning strange attractors from in time series has been accepted by
#NeurIPS2020
. It's been really fun revisiting classic works on chaos in the context of modern ML tools. I’m very grateful to the ML/AI community for considering my work.
My new preprint explores using neural networks to learn “strange attractors” from time series. If we measure a complex system over time, can we infer additional measurement dimensions & discover underlying structure? (1/N)
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For each system, I trained several deep learning models (Transformer, NBEATS, LSTM, neural ODE), plus classical (ARIMA, Linear, FFT) & statistical (Prophet, Exponential Smooth). Deep learning forecasts chaos super well, even w/ noise. Here's epochwise-prediction during training:
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The lake-dwelling protist Stentor uses vortices to trap edible particles. From … with
@PrakashLab
@Viveknprakash
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I wrote an perspective with Yitong Huang & Danny Forger about using machine learning to discover hidden dynamics in biological data! Can machine learning tell us something new about our data, or does it just re-package what we already know?
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Here’s all 131 chaotic systems as an embedding, colored with unsupervised clustering. Includes familiar examples like Lorenz & Mackey-Glass, plus application-specific examples like ecosystems, biochemical networks, & fluid flows. Ranges/pts are meds/errs over many initial conds.
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What does this mean for forecasting? Models that implicitly “lift” input dimensionality (time lags, nonlinear kernels, etc) do better—perhaps chaotic systems act more linear in higher dims? See recent work on Koopman and Perron-Frobenius propagators for dynamics
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Our group successfully completed our first experimental project... installing a new office whiteboard!
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Excited to post our
@NatRevPhys
review on “The multiscale physics of cilia and flagella” We review amazing recent discoveries from the perspective of statistical physics and dynamical systems. It’s been a wonderful journey with
@PrakashLab
and Matt Bull
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A swarm of sea monkeys chasing a blue laser beam
(see paper by Wilhelmus and Dabiri )
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But if you know nothing a priori about your time series, and you have a *lot* of data, new ML models work really well if you tune them carefully. >10 Lyapunov time forecasts would have seemed crazy a few decades ago.
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Not all systems are easy to forecast. I correlated forecast with fractal dimension, Lyapunov exponent, entropy, etc. Lyapunov correlates pretty well with predictability. Seems intuitive, but it’s crazy that a local quantity clearly affects sophisticated long-term forecast algos
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Our new paper on flow visualization appears on the cover of today's
@J_Exp_Biol
! Cheers
@Viveknprakash
@PrakashLab
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My collection of seashells that exhibit cellular automaton patterns
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The biggest takeaway is that the bias-variance tradeoff rules. If you're forecasting a system where you have strict constraints from domain knowledge (Hamiltonian, etc), put them in the model---you'll save yourself compute, need less data, & have less hyperparameter tuning
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However, if we restrict the training history, inductive biases of physics-based models win out. Here, we titrate the amount of training history, re-train each model, and compare forecast quality at 1 Lyapunov time
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It's been a huge privilege to work with and learn from you
@PrakashLab
these past few years. I feel very lucky to be part of such an incredible and creative team. But while I may be gone, my hard drive collection will live on in lab forever...
Congratulations Dr William Gilpin -
@wgilpin0
what a spectacular PhD defense. A combination of beautiful science presented elegantly. And that patiria miniata cake is out of this world! I am so proud to have worked with you William.
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A water drop hits a sandy surface. From a beautiful paper by Zhao et al:
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Our course is fully open-source, and we welcome anyone using or modifying our materials. Pull requests are always welcome (4/4)
Course website:
Course GitHub:
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We can also try applying it to datasets where the underlying attractor is unknown, including patient electrocardiograms, neural data, and even temperature readings of “Old Faithful” geyser eruptions. There are some surprising (but interpretable) low-dimensional dynamics (3/N)
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I’ll be chatting about my NeurIPS paper on using deep learning to reconstruct strange attractors from time series tonight at
#NeurIPS2020
Poster Session 7 (9 PT / 12 ET). Paper here:
Below I used the method to visualize eruptions of the Old Faithful geyser
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Also applications to data-driven modelling; the paper also has examples using all 131 chaotic systems to benchmark neural ODEs, as well as symbolic regression algorithms (N/N)
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A rock-paper-scissors game creates Turing patterns. From a simple model of biodiversity by Reichenbach et al:
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It's been an amazing experience working with so many fun, kind, and creative people these past five years, and learning from Manu's curiousity-driven approach to science. I'm looking forward to learning to ice climb this year.
It’s always a bitter sweet moment to see a lab member leave for new adventures - this time its
@wgilpin0
who is starting as a Qbio Fellow at Harvard👏. Some warm hugs were exchanged, some old jokes reborn. Wish you very best - incredibly proud of everything you have already done!
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My paper showing how to train convolutional neural networks to represent cellular automata appears today in
@PhysRevE
@APSphysics
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Thanks very much to
@PrakashLab
for a wonderful PhD experience, and to
@ApsDbio
for this amazing opportunity!
Excited about William’s
@wgilpin0
invited Award talk at APS March meeting tomorrow for “Outstanding Doctoral Thesis Research in Biological Physics (2020)” - I wish we could celebrate in person; alas we will just have to enjoy ciliary flows virtually.
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We wrapped up the first semester of our open-source computational physics course
@TexasScience
---the students' final projects are pretty cool: (1/N)
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The root of this approach is powerful theorems by Whitney & Takens, which give conditions under which variables can be recovered from the time-history of a system using time lags. These are the basis of popular “state space reconstructions” in ecology & earth science (4/N)
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Other cool things you can do w/ the database: unlike traditional time series, DiffEqs are generative: they can be re-integrated at any granularity, length, or noise. I used the dataset for transfer learning by pretraining a timescale-matched featurizer for a classifier
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Here’s the full ranking across all the models. Distributions correspond to forecast errors across all 131 attractors. Left violin is coarse sampling granularity; Right is fine granularity
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I’ll be at NeurIPS Poster E3 tomorrow 12/10, 8:30 - 10 am PT to discuss my paper on using hundreds of chaotic systems to benchmark forecasting & other time series problems. Turns out classical chaoticity & ML predictability have a subtle relationship
For each system, I trained several deep learning models (Transformer, NBEATS, LSTM, neural ODE), plus classical (ARIMA, Linear, FFT) & statistical (Prophet, Exponential Smooth). Deep learning forecasts chaos super well, even w/ noise. Here's epochwise-prediction during training:
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Colors above are highlighted methods, and I’ll use same colors for ensuing figures. For all figures, error bars are across 135 low-dimensional chaotic systems, and points are single forecast methods (e.g. Transformer, neural ODE, etc)
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Multiscale models like NBEATS or TCN (causal dilated convolutions) seem to do better, perhaps because chaotic systems have continuous spectra. The results hold up across a range of noise levels and granularities (sampling rates)
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Weirdly, the Lyapunov exponent doesn’t correlate empirically with how well different methods perform on different chaotic systems, especially over longer forecasting horizons. More on this in ~*~future work~*~
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In the new method here, an autoencoder is trained on the measurement history, with a new latent-space loss function & regularizer based on influential classical technique by Kennel, Brown, & Abarbanel for determining embedding dimension by avoiding “false neighbors” (5/N)
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We can test this hypothesis by training the network on single coordinates of several well-known strange attractors (Lorenz’s butterfly, Rössler’s Möbius strip, etc), and find that it can reconstruct the full systems pretty well (2/N)
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All the videos above are homework problems: (1) Avalanche activity cascades in a sandpile automaton. (2) Vortex street formed by flow past a cylinder. (3) Turing patterns in the Gray-Scott model
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"The Strange New Science of Chaos" - A 1989 episode of PBS's Nova featuring interviews and elegant demos with Lorenz, Swinney, Shaw, Gollub, et al.
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@oecodynamics
@ricard_sole
Here's a high-res version of this poster on GitHub
The raw code used to make the figure is in the top-level “demos” notebook
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Excerpts from “Chaos in the brickyard,” a 1963 letter to Science by Bernard Forscher about science as “brickmaking” as opposed to "building"
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Chaotic mixing in by two "blinking" vortices. From the Hassan Aref's 1984
@JFluidMech
paper that first discovered chaotic advection
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The intro to the 1960s Japanese TV show “Ultraman” looks just like G.I. Taylor’s classic laminar flow reversal experiment. I wonder if they did the experiment, or if they just reversed the footage?
thanks
@RealCarlosSagan
for sending this.
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We can also compare training costs. Bigger models take longer to train, but do better overall. Each point is a forecast model, error bars are across chaotic systems, and the “tilt” shows the correlation within each method class (no Simpson’s paradox)
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I also compared different metrics of forecast quality. They appear to mostly agree. fwiw, I prefer SMAPE for assessing forecast quality
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Interesting, methods that are better at pointwise forecasts also appear to better reconstruct invariants (manifold dimension, Lyapunov exponents, etc). So probabilistic forecasting and raw accuracy go hand-in-hand.
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An awesome blogpost about my recent preprint, and the broader field of chaos, by
@zkajdan
at RStudio
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My preprint “Cellular automata as convolutional neural networks” appears today on . Here is a video showing the different stages of training with Conway’s Game of Life
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Another group used the adjoint method to map a full-state computational brain model onto a reduced-order Hodgkin-Huxley system (2/4)
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All of our course materials and discussions are on GitHub:
and the main course page is here:
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I gave a talk at
#APSMarch
last week about how baby starfish make chaotic mixing patterns as they swim. We think that they create these beautiful patterns as part of their feeding process:
This work is w/
@PrakashLab
and
@Viveknprakash
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A bit belated, a video of my PhD defense, retroactively titled "Hashing and swimming with chaotic fluid dynamics" for
@PrakashLab
taken by my amazing colleague
@hongquan_li
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Day 1304 of life in Palo Alto: A Tesla with the license plate "AI HYPE" cuts me off in a roundabout.
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Our group's first annual pumpkin carving contest included a variety of surreal entries.
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Why watch fireworks this week when you can instead watch a montage of plants exploding?
c/o
@smithsonian
#july4th
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Our new preprint about higher-order effects in evolutionary dynamics is now online:
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A really stunning new video from
@MBARI_News
showing thousands of brooding octopuses near Monterey Bay
From:
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My new preprint discusses surprising (and solvable) avalanches that occur when oscillators synchronize. Oscillator cascades occur in everything from the human brain to the U.S. power grid, and I show that short-range repulsion is one possible cause
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Our new paper uses reaction-diffusion dynamics to study the spread of Neanderthals and modern humans in Europe:
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A different group implemented a set of stochastic optimizers in JAX, and studied configuration of various many-body systems (3/4)
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@quentinferry1
hi, it's all matplotlib via plt.savefig. I stitch frames into movies with ffmpeg
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@eigensteve
@bingbrunton
Thank you so much—reading your work back in grad school is what got me interested in this whole field in the first place! (I’m sure you hear that a lot)
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our physics PhD program doesn’t require physics undergrad or physics GRE. We’ve had students with undergrads in CS, engineering, bioinformatics, etc and they haven’t found the 4 core courses burdensome. Quals are research-based talks, not written exams 😅 (3/4)
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An amazing piece by
@zkajdan
that implements in R my recent chaos embedding technique (), and uses it to predict heartbeats, neurons, and even geyser eruptions!
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My new paper on chaotic phase transitions in complex ecosystems appears today in
#PLOSCompBio
:
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A worm is slowly pressurized to 15 psi inside a
#microfluidic
device. From my old paper
#celegans
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@FlyingOctopus0
@jm_alexia
I tried this with the ECG embedding below. I kept the points/state static and rotated the embedding. Thank you for the tip!
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Stunning scientific cartoons from physicist Robert Shaw’s 1984 book “The Dripping Faucet As A Model Chaotic System.” Drawn by his brother, Chris Shaw.
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An amazing combination of experiments and theory to study feeding and swimming by cells, by Mathijssen et al.
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@shoyer
@TexasScience
@OdenInstitute
@UTPhysics
That's a really good point, I didn't include any probabilistic models (partly because I didn't think I was knowledgeable enough to benchmark them well).
You pointed out last time that I should think about manifold geometry in addition to raw pointwise accuracy. (1/N)
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A green sea slug that makes literal solar panels from the chloroplasts of algae it eats.
From Rumpho et al:
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An ironic warning on the first page of Internet Archive’s digitization of Oseen’s Hydrodynamics book
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@SumoTail
@TexasScience
@OdenInstitute
@UTPhysics
Hi, here is the repo. I agree that we might be leaning hard on the continuity of time series, versus tabular table
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@shoyer
@TexasScience
@OdenInstitute
@UTPhysics
But I agree that over long periods it's easy to "cheat." My pet theory is that models learn basically to shadow the dominant unstable periodic orbits, since those capture the majority of the measure. It's hard to tell a long-period orbit apart from chaos
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Saw a fascinating talk today by
@KakaniKatija
at
@StanfordEng
about surprisingly complex and beautiful mucus houses built by giant deep sea larvaceans, who can collectively filter all of Monterey Bay in just 13 days!
Papers here:
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Meteor shower and a single night climber on El Capitan in Yosemite National Park, as the Pleiades cluster rises in the background.
@YosemiteNPS
@apod
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Elegant experiments and modelling by
@guille_rochelle
and
@PrakashLab
that demonstrates how disorder can help cilia in the lungs pump fluid
Multi-scale spatial heterogeneity enhances particle clearance in airway ciliary arrays
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On top of earning
@TeamUSA
a medal,
@mirai_nagasu
pulled off an incredible demonstration of conservation of angular momentum
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