Dr. Philipp Meyer

Research scientist,

Coordinator of the Research Focus Data-centric Sciences

As a physicist, I try to describe systems and make predictions. I concentrate on statistical properties and stochastic modeling of complex systems, aiming for intuitive interpretation of data. I am interested in artificial intelligence methods and the exciting task of making data interpretable and understandable.

Lecture: Data Analysis and Stochastic Modelling

Research Interests

Statistics beyond the central limit theorem

The central limit theorem states that the sum of t random variables for large t approaches the Gaussian distribution and the standard deviation scales with t^1/2 if the random variables are

independent (at least after some finite lag time),
identically distributed,
and have a finite variance.

Violation of one of these three premises leads to the Joseph, Moses, and Noah effect, respectively. It can cause anomalous diffusion, where the standard diviation of the particle distribution over time t scales with an anomalous exponent >1/2 or <1/2.

In different projects, we analyzed anomalous diffusive systems, and attributed the observed exponent to the root causes (non-independent increments, not identically distributed increments, or diverging variance). It was shown that for simulated data, deep learning approaches are always superior to analytical methods in inferring anomalous diffusion models.

Return over volume statistics and the Moses effect in S&P 500 data
PG Meyer, M Zamani, H Kantz (2023) Physica A 612, 128497.

Decomposing the effect of anomalous diffusion enables direct calculation of the Hurst exponent and model classification for single random paths
PG Meyer, E Aghion, H Kantz (2022) Journal of Physics A 55(27), 274001.

Objective comparison of methods to decode anomalous diffusion
G Muñoz-Gil et. al. (2022). Nature communications 12(1), 6253.

Moses, Noah and Joseph effects in Lévy walks
E Aghion, PG Meyer, V Adlakha, H Kantz & KE Bassler (2021). New Journal of Physics, 23(2), 023002.

Anomalous diffusion and the Moses effect in an aging deterministic model
PG Meyer, V Adlakha, H Kantz & KE Bassler (2018). New Journal of Physics 20(11), 113033.

Scale-invariant Green-Kubo relation for time-averaged diffusivity
P Meyer, E Barkai & H Kantz (2017). Physical Review E, 96(6), 062122.

Fitting algorithms for autocorrelations

We developped methods for infering dynamical features like characteristic time scales from time series. These methods are based on scale-free representations of the autocorrelation function like detrended fluctuation analysis and the time-averaged mean squared displacement, so they do not overemphasise short time scales.

Time reversal symmetry and the difference between relaxations and building-up periods
PG Meyer & H Kantz (2021). Physical Review E, 104.2, 024208.

Characterizing variability and predictability for air pollutants with stochastic models
PG Meyer, H Kantz & Y Zhou (2021). Chaos, 31(3), 033148.

Identifying characteristic time scales in power grid frequency fluctuations with DFA
PG Meyer, M Anvari & H Kantz (2020). Chaos, 30(1), 013130.

Spring onset forecast using harmonic analysis on daily mean temperature in Germany
Q Deng, PG Meyer, Z Fu & H Kantz (2020). Environmental Research Letters, 15(10), 104069.

A simple decomposition of European temperature variability capturing the variance from days to a decade
PG Meyer & H Kantz (2019). Climate Dynamics, 53(11), 6909-6917.

Inferring characteristic timescales from the effect of autoregressive dynamics on detrended fluctuation analysis
PG Meyer & Kantz (2019). New Journal of Physics, 21(3), 033022.

Reproducing Long‐Range Correlations in Global Mean Temperatures in Simple Energy Balance Models
P Meyer, M Hoell & H Kantz (2018). Journal of Geophysical Research: Atmospheres, 123(9), 4413-4422.

Timescales and effects of measurement error

In many real world systems, characteristic time scales are well-separated. In this case, the dynamics can be decomposed into components, each corresponding to one characteristic time scale. Then aproximative models can be found for each time scale, sequentially.

A particulary relevant example for a special time scale, that should be treated seperately is measurement noise, which is typically un-correlated and thus fluctuates faster than the signal itself.

We developped methods to decompose time series into components and to improve model selection by filtering measurement noise.

Time Scales in the Dynamics of Political Opinions and the Voter Model
PG Meyer, R Metzler (2023). Submitted.

Stochastic processes in a confining harmonic potential in the presence of static and dynamic measurement noise
PG Meyer, R Metzler (2023). New Journal of Physics 25(6), 063003.

Identifying characteristic time scales in power grid frequency fluctuations with DFA
PG Meyer, M Anvari & H Kantz (2020). Chaos, 30(1), 013130.

A simple decomposition of European temperature variability capturing the variance from days to a decade
PG Meyer & H Kantz (2019). Climate Dynamics, 53(11), 6909-6917.

Predictive Modelling

Stochastic models decompose (filter) the dynamics of time series into deterministic and random components. From the deterministic component we can make predictions of future steps. Finding a suitable stochastic model thus solves the problem of forecasting in some cases. For highly non-linear systems or high dimensional input variables, it is more promising to use a machine learning model instead of an analytical model, like neural networks with LSTM layers or simpler approaches to be able to resolve the interactions and non-linearities.

In various projects we worked on predicting the seasonal cycle of temperature, air pollution, and animal movements with different approaches, suitable for the respective data.

Directedeness, correlations, and daily cycles in springbok motion: from data over stochastic models to movement prediction
PG Meyer, AG Cherstvy, H Seckler, R Hering, N Blaum, F Jeltsch & R Metzler (2023) Phys. Rev. Research 5, 043129.